No full-text available
To read the full-text of this research,
you can request a copy directly from the author.
A quantum approach to play asymmetric coordination games
Abstract
We present a quantum approach to play asymmetric coordination games, which are more general than symmetric coordination games such as the Battle of the Sexes game, the Chicken game and the Hawk–Dove game. Our results show that quantum entanglement can help the players to coordinate their strategies.
... The Nash equilibrium are thus (H, D) and (D, H) and (M HD , M HD ). One must also notice that the mixed strategy Nash equilibrium (6.25, 6.25) is much lesser than Pareto optimality payoffs (15,15). ...
... The Nash equilibrium are thus (H, D) and (D, H) and (M HD , M HD ). One must also notice that the mixed strategy Nash equilibrium (6.25, 6.25) is much lesser than Pareto optimality payoffs (15,15). ...
... This scheme has been extended to include various forms of Hawk-Dove game with initially entangled states in Refs. [13][14][15]. The initial state ρ in is taken to be a maximally entangled state, ρ in = |ψ ψ| with ...
S. J. van Enk and R. Pike in PRA 66, 024306 (2002) argue that the equilibrium solution to a quantum game isn't unique but is already present in the classical game itself. In this work, we contest this assertion by showing that a random strategy in a particular quantum (Hawk-Dove) game is unique to the quantum game. In other words, one cannot obtain the equilibrium solution of the quantum Hawk-Dove game in the classical Hawk-Dove game. Moreover, we provide an analytical solution to the quantum strategic form Hawk-Dove game using randomly mixed strategies. The random strategy which we describe is Pareto optimal with their payoff classically unobtainable. We compare quantum strategies to correlated strategies and find that correlated strategies in the quantum Hawk-Dove game or quantum Prisoner's dilemma yield the Nash equilibrium solution.
... Frackiewicz [46] applied the Harsanyi-Selten algorithm to the quantum battle of the sexes game with MW scheme. Situ [47] found that entanglement can improve coordination and outcomes in asymmetric quantum coordination games with MW scheme. Furthermore, Situ [47] introduced a measure of the risk of a NE that depends on the maximum loss of a player due to the opponent's deviation from this NE. ...
... Situ [47] found that entanglement can improve coordination and outcomes in asymmetric quantum coordination games with MW scheme. Furthermore, Situ [47] introduced a measure of the risk of a NE that depends on the maximum loss of a player due to the opponent's deviation from this NE. ...
... The aim of this study is to solve the dilemma of choosing a unique NE in the QPD. We apply the Situ approach [47] and risk-dominance criterion [21,22] and investigate the effects of the dilemma strength parameters and entanglement. ...
The choice of a unique Nash equilibrium (NE) is crucial in theoretical classical and quantum games. The Eiswer-Wilkens-Lewenstein quantization scheme solves the prisoner's dilemma only for high entanglement. At medium entanglement, there are multiple NEs. We investigate the selection of a unique NE in the quantum prisoner's dilemma with variable dilemma strength parameters. The risk-dominance criterion is used. The influence of the dilemma strength parameters and entanglement is emphasized. We found that entanglement completely controls the risk-dominant equilibrium. Entanglement promotes quantum-cooperation in the risk-dominant equilibrium and thus improves its outcome.
... are asymmetric, a rational player chooses the safer NE. The NE risk 29) is the maximum loss when a player insists on his=her NE strategy, while the other deviates. ...
... The second is 1 2 , there are two asymmetric NEs., namely,Û A ð1Þ Û B ð0Þ andÛ A ð0Þ Û B ð1Þ. Since neither can dominate the other, we use the NE risk 29) to determine which one will prevail. The NE risk for every NE is determined according to the following procedure. ...
... exist, namely,Û A ð0Þ Û B ð1Þ and U A ð1Þ Û B ð0Þ. We use the NE risk 29) to determine the safest NE. When player A insists on using the NEÛ A ð0Þ Û B ð1Þ and player B deviates, the risk becomes: 1 2 like the case D r > D g . ...
... are asymmetric, a rational player chooses the safer NE. The NE risk 29) is the maximum loss when a player insists on his=her NE strategy, while the other deviates. ...
... The second is 1 2 , there are two asymmetric NEs., namely,Û A ð1Þ Û B ð0Þ andÛ A ð0Þ Û B ð1Þ. Since neither can dominate the other, we use the NE risk 29) to determine which one will prevail. The NE risk for every NE is determined according to the following procedure. ...
... exist, namely,Û A ð0Þ Û B ð1Þ and U A ð1Þ Û B ð0Þ. We use the NE risk 29) to determine the safest NE. When player A insists on using the NEÛ A ð0Þ Û B ð1Þ and player B deviates, the risk becomes: 1 2 like the case D r > D g . ...
When it comes to global issues, interactions among participants are always asymmetric due to resource availability
and environmental impacts. Therefore, it is important to analyze decision-making among participants with different
strategies. We introduce quantum prisoner’s dilemma in asymmetric strategy spaces. The formulation with two dilemma
strength parameters is considered, and the Eisert–Wilkens–Lewenstein quantization scheme is applied. The properties of
Nash equilibrium are studied for all possible cases of the values of the dilemma strength parameters and for each level of
asymmetry. A solution for the dilemma can be obtained only in some extreme limits where the environmental influence
is the largest. Consequently, it is unlikely to find a solution to the dilemma in the quantum domain with asymmetric
strategy spaces. Therefore, strategies need to be standardized when dealing with global issues.
... The chief distinguishing feature of quantum game theory is that it exploits the remarkable properties of quantum mechanics, the entanglement, to get results that are classically impossible. A number of different categories of classical games have been converted into the realm of quantum mechanics, such as strategic games [1][2][3][4][5][6][7], extensive games [8][9][10][11][12][13], Bayesian games [14][15][16][17][18], multi-player games [19,20], evolutionary games [21] and iterated games [22][23][24][25]. ...
... Then, player A is stationary and player B moves with a uniform acceleration. The Minkowski vacuum state could be expressed in terms of the Rindler region I and region I I states [43] |0 M = cos(r )|0 I |0 I I + sin(r )|1 I |1 I I (4) The excited state in Minkowski spacetime is related to Rindler modes as follows [43] |1 M = |1 I |0 I I (5) Note that the observers in Rindler region I and region I I are causally disconnected from each other, where cos(r ) = (e −2πωc/a + 1) −1/2 with a the Bob's acceleration. The parameter r ∈ [0, π/4] as a ranges from 0 to infinity. ...
... From the accelerated player B's frame, the state of player B should be expanded as Eqs. (4) and (5). Thus, the state of Eq. (3) changes to ...
In this paper, we demonstrate a method to improve the payoffs of players in relativistic quantum Bayesian game using partial-collapse measurement. We consider two cases. (Only Unruh effect exists, or both Unruh effect and quantum noise are taken into account.) The results show that the payoffs of players can be enhanced greatly in both cases. The payoffs of two players could be above the classical payoffs by choosing the appropriate partial-collapse measurement strengths. It is noted that for the case only Unruh effect exists, the Unruh effect could be eliminated by using partial-collapse measurement and thus the payoffs of two players are almost completely protected.
... The Nash equilibrium are thus (H, D) and (D, H) and (M HD , M HD ). One must also notice that the mixed strategy Nash equilibrium (6.25, 6.25) is much lesser than Pareto optimality payoffs (15,15). ...
... The Nash equilibrium are thus (H, D) and (D, H) and (M HD , M HD ). One must also notice that the mixed strategy Nash equilibrium (6.25, 6.25) is much lesser than Pareto optimality payoffs (15,15). ...
... This scheme has been extended to include various forms of Hawk-Dove game with initially entangled states in Refs. [13][14][15]. The initial state ρ in is taken to be a maximally entangled state, ρ in = |ψ ψ| with ...
S. J. van Enk and R. Pike in PRA 66, 024306 (2002), argue that the equilibrium solution to a quantum game isn't unique but is already present in the classical game itself. In this work, we contest this assertion by showing that a random strategy in a particular quantum (Hawk-Dove) game is unique to the quantum game. In other words the equilibrium solution of the quantum Hawk-Dove game can not be obtained in the classical Hawk-Dove game. Moreover, we provide an analytical solution to the quantum strategic form Hawk-Dove game using random mixed strategies. The random strategies which we describe are Pareto optimal with their payoff's classically unobtainable. We compare the quantum strategies to correlated strategies and find that correlated strategies in quantum Hawk-Dove game or quantum Prisoner's dilemma yield the Nash equilibrium solution.
... Game theory [1], a tool for rational decision making in conflict situations, is commonly used in economics, biology and physics. By introducing quantum mechanics into game theory, began from the seminal paper of Meyer [2], number of classical games have been converted to quantum versions [2][3][4][5][6][7][8][9][10][11]. A new field has been created: quantum game theory [2] which deals with classical games in the domain of quantum mechanics. ...
... Quantum versions of Chicken game have been studied under the EWL scheme [6] and the MW scheme [9,10]. This section follows the EWL scheme [6], in which possible outcomes of the classical strategies D (defect) and C (cooperate) are denoted as two basis qubit state |D (|1 for simplicity) and |C (|0 for simplicity) in the 2-dimensional Hilbert space. ...
Quantum systems are easily influenced by ambient environments. Decoherence is generated by system interaction with external environment. In this paper, we analyse the effects of decoherence on quantum games with Eisert-Wilkens-Lewenstein (EWL) (Eisert et al., Phys. Rev. Lett. 83(15), 3077 1999) and Marinatto-Weber (MW) (Marinatto and Weber, Phys. Lett. A 272, 291 2000) schemes. Firstly, referring to the analytical approach that was introduced by Eisert et al. (Phys. Rev. Lett. 83(15), 3077 1999), we analyse the effects of decoherence on quantum Chicken game by considering different traditional noisy channels. We investigate the Nash equilibria and changes of payoff in specific two-parameter strategy set for maximally entangled initial states. We find that the Nash equilibria are different in different noisy channels. Since Unruh effect produces a decoherence-like effect and can be perceived as a quantum noise channel (Omkar et al., arXiv:1408.1477v1), with the same two parameter strategy set, we investigate the influences of decoherence generated by the Unruh effect on three-player quantum Prisoners’ Dilemma, the non-zero sum symmetric multiplayer quantum game both for unentangled and entangled initial states. We discuss the effect of the acceleration of noninertial frames on the the game’s properties such as payoffs, symmetry, Nash equilibrium, Pareto optimal, dominant strategy, etc. Finally, we study the decoherent influences of correlated noise and Unruh effect on quantum Stackelberg duopoly for entangled and unentangled initial states with the depolarizing channel. Our investigations show that under the influence of correlated depolarizing channel and acceleration in noninertial frame, some critical points exist for an unentangled initial state at which firms get equal payoffs and the game becomes a follower advantage game. It is shown that the game is always a leader advantage game for a maximally entangled initial state and there appear some points at which the payoffs become zero.
... Meyer found that a player who implemented a quantum strategy could increase his expected payoff by using a PQ penny flipover game 22 . Furthermore, a lot of research works have proven that quantum games are greatly different from their classical counterparts [23][24][25][26][27][28][29][30][31] , which thus indicates that quantum games open up a new way to study the dilemmas in the classical game theory. ...
... $ B (p * = 1, q * = 0) ∈ [2.5, 10.625], $ A+B (p * = 1, q * = 0) ∈ [−6, 22.667]. (29) Similarly, we find that in this case of (p * = 1, q * = 0) being a NE, the quantum version of inspection game is still not able to implement a Pareto improvement on the mixed-strategy NE of classical inspection game. The maximum joint payoff of A and B is 21 when |a| 2 = 0.3, |b| 2 = 0.45, |c| 2 = 0.1, |d| 2 = 0.15, at the same time $ A (p * = 1, q * = 0) = 16 and$ B (p * = 1, q * = 0) = 5. ...
Quantum game theory is a new interdisciplinary field between game theory and
physical research. In this paper, we extend the classical inspection game into
a quantum game version by quantizing the strategy space and importing
entanglement between players. Our result shows that the quantum inspection game
has various Nash equilibrium depending on the initial quantum state of the
game. It is also shown that quantization can respectively help each player to
increase his own payoff, yet fails to bring Pareto improvement for the
collective payoff in the quantum inspection game.
... While in the scheme for 2 × 2 games the result of the game depends on six real parameters (each players' strategy is a unitary operator from SU (2), and it is defined by three real parameters), the EWL-type scheme for 3 × 3 games would already require 16 parameters to take into account [3], [4]. One way to avoid cumbersome calculations when studying a game in the quantum domain was presented in [5] (see also recent papers [6], [7] [8] and [9] based on this scheme). The authors defined a model (the MW scheme) for quantum game where the players' unitary strategies were restricted to the identity and bit-flip operator. ...
We give a strict mathematical description for a refinement of the Marinatto-Weber quantum game scheme. The model allows the players to choose projector operators that determine the state on which they perform their local operators. The game induced by the scheme generalizes finite strategic form game. In particular, it covers normal representations of extensive games, i.e., strategic games generated by extensive ones. We illustrate our idea with an example of extensive game and prove that rational choices in the classical game and its quantum counterpart may lead to significantly different outcomes.
... Although Marinatto-Weber's discussion brought out an interesting point of view, their analysis restricts the choices of the players as pointed out by Benjamin [20]. Numerous theoretical discussions attempted to show its potentiality [21][22][23][24][25], highlighting the use of a general initial quantum state [26], arguing the omission of a disentangling quantum gate J † to maintain the quantum game in its highest correlated regime where the dilemma does not exist [20,27], using the Harsanyi-Selten algorithm to accomplish an ultimate solution [28] and playing asymmetric coordination games [29]. Out of these previously cited, the most important is about the omission of a disentangling quantum gate. ...
Quantum games have gained much popularity in the last two decades. Many of these quantum games are a redefinition of iconic classical games to fit the quantum world, and they gain many different properties and solutions in this different view. In this letter, we attempt to find a solution to an asymmetric quantum game which still troubles quantum game researchers, the quantum battle of the sexes. To achieve that, we perform an analysis using the Eisert–Wilkens–Lewenstein protocol for this asymmetric game. The protocol highlights two solutions for the game, which solve the dilemma and satisfy the pareto-optimal definition, unlike previous reports that rely on Nash equilibrium. We perform an experimental implementation using the NMR technique in a two-qubit system. Our results eliminate dilemmas on the quantum battle of the sexes and provide us with arguments to elucidate that the Eisert–Wilkens–Lewenstein protocol is not restricted to symmetric games at the quantum regime.
... Although Marinatto-Weber's discussion brought out an interesting point of view, their analysis restricts the choices of the players as pointed out by Benjamin [17]. Numerous theoretical discussions attempted to show its potentiality [18,19,20,21], highlighting the use of a general initial quantum state [22], arguing the omission of a disentangling quantum gate J † to maintain the quantum game in its highest correlated regime where the dilemma does not exist [17,23], using the Harsanyi-Selten algorithm to accomplish an ultimate solution [24] and playing asymmetric coordination games [25]. Out of these previously cited, the most important is about the omission of a disentangling quantum gate. ...
Quantum games have gained much popularity in the last two decades. Many of these quantum games are a redefinition of iconic classical games to fit the quantum world, and they gain many different properties and solutions in this different view. In this letter, we attempt to find a solution to an asymmetric quantum game which still troubles quantum game researchers, the quantum battle of the sexes. To achieve that, we perform an analysis using the Eisert-Wilkens-Lewenstein's protocol for this asymmetric game. The protocol highlights two solutions for the game, which solve the dilemma and satisfy the Pareto-optimal definition, unlike previous reports that rely on Nash equilibrium. We perform an experimental implementation using the NMR technique in a two-qubit system. Our results eliminate dilemmas on the quantum battle of the sexes and provide us with arguments to elucidate that the Eisert-Wilkens-Lewenstein's protocol is not restricted to symmetric games when at the quantum regime.
... We use Quantum Composer, the graphical user interface of IBM Quantum Experience, to assemble the quantum circuits for preparing the entangled states and making appropriate measurements. The backend is the ibmqx4 processor with five physical qubits labeled by q[0], q [1], q [2], q [3], q [4]. Each measurement setting (i.e., each input x) of each game corresponds to a specific quantum circuit, which is run 8192 times to produce a probability distribution of the measurement result p(y|x). ...
Conflicting interest nonlocal games are special Bayesian games played by noncooperative players without communication. In recent years, some conflicting interest nonlocal games have been proposed where quantum advice can help players to obtain higher payoffs. In this work we perform an experiment of six conflicting interest nonlocal games using the IBM quantum computer made up of five superconducting qubits. The experimental results demonstrate quantum advantage in four of these games, whereas the other two games fail to showcase quantum advantage in the experiment.
... General pay-off matrices [7] and other noise types [16,[29][30][31] are to come under scrutiny in subsequent studies on iterated quantum games in the spatial context. Other quantization schemes [32][33][34][35], multiparty games [36,37] as well as games with imperfect information [23,[38][39][40][41] deserve particular studies. ...
The dynamics of a spatial quantum formulation of the iterated Samaritan’s dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e. with local and synchronous interaction. The game is assessed in fair and unfair contests, in noiseless scenarios and with disrupting quantum noise.
... Other noise types [14] are to come for scrutiny in subsequent studies on iterated quantum games in the spatial context, to be extended to asymmetric games such as the Battle of the Sexes [5,6] , the Samaritan game [19] and to the quantum version of the penny flip game [13]. Other quantization schemes [16,17,22] as well as games with imperfect information [2,23,24] also deserve further particular studies. ...
The disrupting effect of quantum noise on the dynamics of a spatial quantum formulation of the iterated prisoner’s dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. It is concluded in this article that quantum noise induces in fair games the need for higher entanglement in order to make possible the emergence of the strategy pair (Q, Q), which produces the same payoff of mutual cooperation. In unfair quantum versus classic player games, quantum noise delays the prevalence of the quantum player.
... Quantum resources such as quantum superposition and quantum entanglement offer additional strategies, which can not only solve dilemmas occurring in classical games, but also improve the outcome of some games. Since the pioneering work of Meyer [2], many different kinds of games have been investigated on the basis of quantum game theory [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. ...
In this work, we study the payoffs of quantum Samaritan’s dilemma played with the thermal entangled state of XXZ spin model in the presence of Dzyaloshinskii-Moriya (DM) interaction. We discuss the effect of anisotropy parameter, strength of DM interaction and temperature on quantum Samaritan’s dilemma. It is shown that although increasing DM interaction and anisotropy parameter generate entanglement, players payoffs are not simply decided by entanglement and depend on other game components such as strategy and payoff measurement. In general, Entanglement and Alice’s payoff evolve to a relatively stable value with anisotropy parameter, and develop to a fixed value with DM interaction strength, while Bob’s payoff changes in the reverse direction. It is noted that the augment of Alice’s payoff compensates for the loss of Bob’s payoff. For different strategies, payoffs have different changes with temperature. Our results and discussions can be analogously generalized to other 2 × 2 quantum static games in various spin models.
... So far many different categories of games have been investigated in the view of quantum game theory. Among these are strategic games [2][3][4][5][6][7][8][9][10], extensive games [11][12][13][14][15], Bayesian games [16][17][18][19][20][21][22][23], multi-player games [24][25][26][27], and iterated games played in the cellular automata manner [28][29][30][31][32]. ...
We study how quantum noise affects the solution of quantum Samaritan’s dilemma. Serval most common dissipative and nondissipative noise channels are considered as the model of the decoherence process. We find that the solution of quantum Samaritan’s dilemma is stable under the influence of the amplitude damping, the bit flip and the bit-phase flip channel.
... The prisoner's dilemma has been already studied in the spatial quantum relativistic scenario in [7], but other games, particularly the Samaritan's dilemma [18] and asymmetric coordination games [19], as well as other quantization schemes [20][21][22][23][24] deserve particular studies in the spatial context. The effect of quantum noise [5], games with imperfect information [25,10,26] and QR games with both players accelerated are to come for scrutiny in subsequent studies. ...
The effect of variable entangling on the dynamics of a spatial quantum relativistic formulation of the iterated battle of the sexes game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests. Despite the full range of quantum parameters initially accessible, they promptly converge into fairly stable configurations, that often show rich spatial structures in simulations with no negligible entanglement.
... Other noise types [14] are to come for scrutiny in subsequent studies on iterated quantum games in the spatial context, to be extended to asymmetric games such as the Battle of the Sexes [5,6,30], or the Samaritan game [15]. Other quantization schemes [18,19,25] as well as games with imperfect information [2,24,[26][27][28] deserve particular studies. ...
The disrupting effect of quantum noise on the dynamics of a spatial quantum relativistic formulation of the iterated prisoner’s dilemma game with variable entangling is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests.
... Other quantization schemes [16,17,21] deserve particular studies in the spatial context. In particular the scheme introduced by Marinatto and Weber [15] . ...
The effect of variable entangling on the dynamics of a spatial quantum relativistic formulation of the iterated prisoner’s dilemma game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The game is assessed in fair and unfair contests.
... While in the scheme for 2 × 2 games the result of the game depends on six real parameters (each players' strategy is a unitary operator from SU (2), and it is defined by three real parameters), the EWL-type scheme for 3×3 games would already require 16 parameters to take into account [3,4]. One way to avoid cumbersome calculations when studying a game in the quantum domain was presented in [5] (see also recent papers [6][7][8] and [9] based on this scheme). The authors defined a model (the MW scheme) for quantum game where the players' unitary strategies were restricted to the identity and bit-flip operator. ...
We give a strict mathematical description for a refinement of the Marinatto–Weber quantum game scheme. The model allows the players to choose projector operators that determine the state on which they perform their local operators. The game induced by the scheme generalizes finite strategic-form game. In particular, it covers normal representations of extensive games, i.e., strategic games generated by extensive ones. We illustrate our idea with an example of extensive game and prove that rational choices in the classical game and its quantum counterpart may lead to significantly different outcomes.
... Quantization approaches have already been adopted to many classical game models, for example prisoner's dilemma [26,28], battle of the sexes [27], Hawk-Dove game [29,30], and so on [31][32][33][34][35][36][37][38]. Through quantization, these game models show some different characteristics, compared with their classical counterparts. ...
Quantization becomes a new way to study classical game theory since quantum
strategies and quantum games have been proposed. In previous studies, many
typical game models, such as prisoner's dilemma, battle of the sexes, Hawk-Dove
game, have been investigated by using quantization approaches. In this paper,
several game models of opinion formations have been quantized based on the
Marinatto-Weber quantum game scheme, a frequently used scheme to convert
classical games to quantum versions. Our results show that the quantization can
change fascinatingly the properties of some classical opinion formation game
models so as to generate win-win outcomes.
The choice of a unique Nash equilibrium (NE) is crucial in theoretical classical and quantum games. The Eisert–Wilkens–Lewenstein quantization scheme solves the prisoner’s dilemma only for high entanglement. At medium entanglement, there are multiple NEs. We investigate the selection of a unique NE in this case. A game with variable dilemma strength parameters is considered, and the risk-dominance criterion is used. The influence of the dilemma strength parameters and entanglement is emphasized. We found that entanglement completely controls the risk-dominant equilibrium. Entanglement promotes quantum-cooperation in the risk-dominant equilibrium and thus improves its outcome.
Most games in the real world are asymmetric, and participants can have different conditions or strategies, depending on the available resources. In this work, the quantum prisoner’s dilemma with two dilemma strength parameters is studied. Two examples of asymmetric strategy spaces are considered. We show that, most of the obtained Nash equilibria are not Pareto optimal. Therefore, the classical dilemma can still exist in the quantum regime with asymmetric strategy spaces. These results can be applied to real-world situations, when global issues requiring the interaction of agents from different environments exist.
Quantum systems are easily affected by external environment. In this paper, we investigate the influences of external massless scalar field to quantum Prisoners’ Dilemma (QPD) game. We firstly derive the master equation that describes the system evolution with initial maximally entangled state. Then, we discuss the effects of a fluctuating massless scalar field on the game’s properties such as payoff, Nash equilibrium, and symmetry. We find that for different game strategies, vacuum fluctuation has different effects on payoff. Nash equilibrium is broken but the symmetry of the game is not violated.
Recently, the first conflicting interest quantum game based on the nonlocality property of quantum mechanics has been introduced in A. Pappa, N. Kumar, T. Lawson, M. Santha, S. Y. Zhang, E. Diamanti and I. Kerenidis, Phys. Rev. Lett. 114 (2015) 020401. Several quantum games of the same genre have also been proposed subsequently. However, these games are constructed from some well-known Bell inequalities, thus are quite abstract and lack of realistic interpretations. In the present paper, we modify the common interest land bidding game introduced in N. Brunner and N. Linden, Nat. Commun. 4 (2013) 2057, which is also based on nonlocality and can be understood as two companies collaborating in developing a project. The modified game has conflicting interest and reflects the free rider problem in economics. Then we show that it has a fair quantum solution that leads to better outcome. Finally, we study how several types of paradigmatic noise affect the outcome of this game.
In this work, we mainly analyse the dynamics of quantum coherence, entanglement, geometric quantum discord and payoffs of a two-player quantum game under noisy environment. Our results indicate that unitary strategies do not change resource measures but change players' payoffs, and entangled operator changes both. Different measures have different variations with noise parameter and entanglement parameter. The behaviors of all quantifiers and payoffs in Markovian regime are different from the case of the non-Markovian regime. The case when only one of the two players is affected by noise gives different results from the case when the noise acts on both players. We find that the game symmetry is broken under noisy environment.
Noise effects can be harmful to quantum information systems. In the present paper, we study noise effects in the context of quantum games with incomplete information, which have more complicated structure than quantum games with complete information. The effects of several paradigmatic noises on three newly proposed conflicting interest quantum games with incomplete information are studied using numerical optimization method. Intuitively noises will bring down the payoffs. However, we find that in some situations the outcome of the games under the influence of noise effects are counter-intuitive. Sometimes stronger noise may lead to higher payoffs. Some properties of the game, like quantum advantage, fairness and equilibrium, are invulnerable to some kinds of noises.
The effect of variable entangling on the dynamics of a spatial quantum formulation of the iterated battle of the sexes game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The effect of spatial structure is assessed when allowing the players to adopt quantum and classical strategies, both in the two and three parameter strategy spaces.
We study how Unruh effect and quantum noise affect the payoffs of a quantum conflicting interest Bayesian game. Three types of noisy channels, i.e., the amplitude damping channel, the depolarizing channel and the phase damping channel, are employed to model the decoherence processes. We find that Unruh effect weakens the payoffs in the quantum game and the quantum payoffs are lower than the classical payoffs when the acceleration parameter is large enough. However, the variation of the payoffs with the decoherence parameter is not always monotonic. Sometimes more decoherence may lead to higher payoffs.
The dynamics of a spatial quantum formulation of the iterated battle of the sexes game with imperfect information is studied in this work. The game is played with variable entangling in a cellular automata manner, i.e. with local and synchronous interaction. The effect of spatial structure is assessed in fair and unfair scenarios.
In a two-stage repeated classical game of prisoners' dilemma the knowledge
that both players will defect in the second stage makes the players to defect
in the first stage as well. We find a quantum version of this repeated game
where the players decide to cooperate in the first stage while knowing that
both will defect in the second.
We study two forms of a symmetric cooperative game played by three players, one classical and other quantum. In its classical form making a coalition gives advantage to players and they are motivated to do so. However, in its quantum form the advantage is lost and players are left with no motivation to make a coalition.
In economics, duopoly is a market dominated by two firms large enough to influence the market price. Stackelberg presented a dynamic form of duopoly that is also called the ''leader-follower'' model. We give a quantum perspective on the Stackelberg duopoly that gives a backwards-induction outcome same as the Nash equilibrium in the static form of duopoly also known as the Cournot's duopoly. We find the two-qubit quantum pure states required for this purpose.
We consider a slightly modified version of the Rock-Scissors-Paper (RSP) game from the point of view of evolutionary stability. In its classical version the game has a mixed Nash equilibrium (NE) not stable against mutants. We find a quantized version of the RSP game for which the classical mixed NE becomes stable.
We study the influence of entanglement and correlated noise using correlated amplitude damping, depolarizing and phase damping channels on the quantum Stackelberg duopoly. Our investigations show that under the influence of an amplitude damping channel a critical point exists for an unentangled initial state at which firms get equal payoffs. The game becomes a follower advantage game when the channel is highly decohered. Two critical points corresponding to two values of the entanglement angle are found in the presence of correlated noise. Within the range of these limits of the entanglement angle, the game is a follower advantage game. In the case of a depolarizing channel, the payoffs of the two firms are strongly influenced by the memory parameter. The presence of quantum memory ensures the existence of the Nash equilibrium for the entire range of decoherence and entanglement parameters for both the channels. A local maximum in the payoffs is observed which vanishes as the channel correlation increases. Moreover, under the influence of the depolarizing channel, the game is always a leader advantage game. Furthermore, it is seen that the phase damping channel does not affect the outcome of the game.
In game theory, an Evolutionarily Stable Set (ES set) is a set of Nash
Equilibrium (NE) strategies that give the same payoffs. Similar to an
Evolutionarily Stable Strategy (ES strategy), an ES set is also a strict NE.
This work investigates the evolutionary stability of classical and quantum
strategies in the quantum penny flip games. In particular, we developed an
evolutionary game theory model to conduct a series of simulations where a
population of mixed classical strategies from the ES set of the game were
invaded by quantum strategies. We found that when only one of the two players'
mixed classical strategies were invaded, the results were different. In one
case, due to the interference phenomenon of superposition, quantum strategies
provided more payoff, hence successfully replaced the mixed classical
strategies in the ES set. In the other case, the mixed classical strategies
were able to sustain the invasion of quantum strategies and remained in the ES
set. Moreover, when both players' mixed classical strategies were invaded by
quantum strategies, a new quantum ES set emerged. The strategies in the quantum
ES set give both players payoff 0, which is the same as the payoff of the
strategies in the mixed classical ES set of this game.
Quantum generalizations of conventional games broaden the range of available strategies, which can help improve outcomes for the participants. With many players, such quantum games can involve entanglement among many states which is difficult to implement, especially if the states must be communicated over some distance. This paper describes a quantum approach to the economically significant n-player public goods game that requires only two-particle entanglement and is thus much easier to implement than more general quantum mechanisms. In spite of the large temptation to free ride on the efforts of others in the original game, two-particle entanglement is sufficient to give near optimal expected payoff when players use a simple mixed strategy for which no player can benefit by making different choices. This mechanism can also address some heterogeneous preferences among the players.
PACS: 03.67-a; 02.50Le; 89.65.Gh
Game theory suggests quantum information processing technologies could provide useful new economic mechanisms. For example,
using shared entangled quantum states can alter incentives so as to reduce the free-rider problem inherent in economic contexts
such as public goods provisioning. However, game theory assumes players understand fully the consequences of manipulating
quantum states and are rational. Its predictions do not always describe human behavior accurately. To evaluate the potential
practicality of quantum economic mechanisms, we experimentally tested how people play the quantum version of the prisoner’s
dilemma game in a laboratory setting using a simulated version of the underlying quantum physics. Even without formal training
in quantum mechanics, people nearly achieve the payoffs theory predicts, but do not use mixed-strategy Nash equilibria predicted
by game theory. Moreover, this correspondence with game theory for the quantum game is closer than that of the classical game.
Both classical and quantum version of two models of price competition in duopoly market, the one is realistic and the other is idealized, are investigated. The pure strategy Nash equilibria of the realistic model exists under stricter condition than that of the idealized one in the classical form game. This is the problem known as Edgeworth paradox in economics. In the quantum form game, however, the former converges to the latter as the measure of entanglement goes to infinity. Comment: 8 pages, 1 figure
We present the unique solution to the Quantum Battle of the Sexes game. We
show the best result which can be reached when the game is played according to
Marinatto and Weber's scheme. The result which we put forward does not
surrender the criticism of previous works on the same topic.
We investigate the quantization of non-zero sum games. For the particular case of the Prisoners' Dilemma we show that this game ceases to pose a dilemma if quantum strategies are allowed for. We also construct a particular quantum strategy which always gives reward if played against any classical strategy.
In these lecture notes we investigate the implications of the identification
of strategies with quantum operations in game theory beyond the results
presented in [J. Eisert, M. Wilkens, and M. Lewenstein, Phys. Rev. Lett. 83,
3077 (1999)]. After introducing a general framework, we study quantum games
with a classical analogue in order to flesh out the peculiarities of game
theoretical settings in the quantum domain. Special emphasis is given to a
detailed investigation of different sets of quantum strategies.
We describe human-subject laboratory experiments on probabilistic auctions based on previously proposed auction protocols involving the simulated manipulation and communication of quantum states. These auctions are probabilistic in determining which bidder wins, or having no winner, rather than always having the highest bidder win. Comparing two quantum protocols in the context of first-price sealed bid auctions, we find the one predicted to be superior by game theory also performs better experimentally. We also compare with a conventional first price auction, which gives higher performance. Thus to provide benefits, the quantum protocol requires more complex economic scenarios such as maintaining privacy of bids over a series of related auctions or involving allocative externalities.
The dynamics of a spatial quantum formulation of the iterated battle of the sexes game is studied in this work. The game is played in the cellular automata manner, i.e., with local and synchronous interaction. The effect of spatial structure is assessed when allowing the players to adopt quantum strategies that are no restricted to any particular subset of the possible strategies.
Recently Marinatto and Weber introduced an interesting new scheme for quantizing games, and applied their scheme to the famous game 'Battle of the Sexes'. In this Comment we make two observations: (a) the overall quantization scheme is fundamentally very similar to a previous scheme proposed by Eisert et al., and (b) in contrast to a main claim of the paper, the quantum Battle of the Sexes game does not have a unique solution - a similar dilemma exists in both the classical and the quantum versions. Comment: 2 pages, 1 figure
We quantize prisoner dilemma in presence of collective dephasing with
dephasing rate . It is shown that for two parameters set of strategies
is Nash equilibrium below a cut-off value of time. Beyond this
cut-off it bifurcates into two new Nash equilibria and . Furthermore for maximum value of decoherence \ and also become Nash equilibria. At this stage the game has four Nash
equilibria. On the other hand for three parameters set of strategies there is
no pure strategy Nash equilibrium however there is mixed strategy (non unique)
Nash equilibrium that is not affected by collective dephasing..
We extend the concept of a classical two-person static game to the quantum domain, by giving an Hilbert structure to the space of classical strategies and studying the Battle of the Sexes game. We show that the introduction of entangled strategies leads to a unique solution of this game.
We present a scheme for playing quantum repeated 2 × 2 games based on Marinatto and Weber's approach to quantum games. As a potential application, we study the twice repeated Prisoner's Dilemma game. We show that results not available in the classical game can be obtained when the game is played in the quantum way. Before we present our idea, we comment on the previous scheme of playing quantum repeated games proposed by Iqbal and Toor. We point out the drawbacks that make their results unacceptable.
We analyze quantum game with correlated noise through generalized quantization scheme. Four different combinations on the basis of entanglement of initial quantum state and the measurement basis are analyzed. It is shown that the advantage that a quantum player can get by exploiting quantum strategies is only valid when both the initial quantum state and the measurement basis are in entangled form. Furthermore, it is shown that for maximum correlation the effects of decoherence diminish and it behaves as a noiseless game. Comment: 12 pages
We analysed quantum version of the game battle of sexes using a general initial quantum state. For a particular choice of initial entangled quantum state it is shown that the classical dilemma of the battle of sexes can be resolved and a unique solution of the game can be obtained. Comment: Revised, Latex, 9 pages, no figure, corresponding author's email: el1anawaz@qau.edu.pk
This is a reply to the paper by S.C.Benjamin, quant-ph/0008127. Comment: 2 pages, Latex, submitted to Phys. Lett. A
Prisoners' dilemma in the presence of collective dephasing A quantum approach to play asymmetric coordination games
- A Nawaz
Nawaz, A.: Prisoners' dilemma in the presence of collective dephasing. J. Phys. A: Math. Theor. 45, 195304 (2012) A quantum approach to play asymmetric coordination games