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Bayesian Foundations for Game Theory? A Comment on "Making Decisions in Large Worlds" by Ken Binmore
Abstract
Comment on the article "Making Decision in Large Worlds" by Ken Binmore
... Allais' parodox and Ellsberg's paradox [5] are examples of situations where decision makers violate the expected utility hypothesis. More recently, Binmore [2] and Lec and Leroux [8] explored more philosophical questions on inaccuracy, arbitrariness, and illegitimacy of Bayesianism in games. The behavioral sociology literature also reports that Bayesian strategies fail to occur in some real world games [10]. ...
The paper studies one-shot two-player games with non-Bayesian uncertainty. The players have an attitude that ranges from optimism to pessimism in the face of uncertainty. Given the attitudes, each player forms a belief about the set of possible strategies of the other player. If these beliefs are consistent, one says that they form an uncertainty equilibrium. One then considers a two-phase game where the players first choose their attitude and then play the resulting game. The paper illustrates these notions with a number of games where the approach provides a new insight into the plausible strategies of the players.
... Allais' parodox [2] and Ellsberg's paradox [18] are examples of situations where decision makers violate the expected utility hypothesis. More recently, Binmore [12] and Lec and Leroux [25] explored more philosophical questions on inaccuracy, arbitrariness, and illegitimacy of Bayesianism in games. The behavioral sociology literature also reports that Bayesian strategies fail to occur in some real world games [40] . ...
The thesis studies games with non-probabilistic uncertainty about some parameters that affect the rewards of the players. The goal is to understand whether players should be optimistic or pessimistic in such situations. The first chapter provides a brief overview of the standard solution concepts in Game Theory. The second chapter proposes a model where the players are strategic in choosing their attitude (degree of optimism), instead of having an intrinsic risk aversion. The idea is that Alice may be able to take advantage of Bob's pessimism, in which case Bob should not be pessimistic. The chapter presents a few examples of two-player non-cooperative games where the agents have a dominant attitude (e.g., optimism), regardless of the unknown private information of the opponent. The chapter also analyses a Cournot duopoly game where each firm has confidential knowledge of its production cost. In the symmetric case, it is shown that pessimism is never a dominant attitude. Finally, the chapter defines a robust attitude and the price of uncertainty, and analyzes them in the Cournot duopoly game. The third chapter studies a simple wireless network with two relay nodes that cooperate to forward information to a common destination. For a range of success probabilities, only the node with the largest success probability should relay packets to avoid collisions at the destination. However, the success probability of a node is known initially only to that node. To improve the performance of the network, the nodes exchange link state messages through a control channel that is not fully reliable. The chapter studies a protocol where each node tries to protect the performance against the worst possible choice of the other node. The performance of that protocol does not converge as the relays exchange more and more link state messages. Essentially, the relay nodes use an excess of caution. The chapter studies another protocol where each relay node ignores the possible states of knowledge of the other node. The throughput of this less cautious protocol converges to the maximum possible value.
... Allais' parodox and Ellsberg's paradox [5] are examples of situations where decision makers violate the expected utility hypothesis. More recently, Binmore [2] and Lec and Leroux [8] explored more philosophical questions on inaccuracy, arbitrariness, and illegitimacy of Bayesianism in games. The behavioral sociology literature also reports that Bayesian strategies fail to occur in some real world games [10]. ...
The paper studies one-shot two-player games with non-Bayesian uncertainty.
The players have an attitude that ranges from optimism to pessimism in the face
of uncertainty. Given the attitudes, each player forms a belief about the set
of possible strategies of the other player. If these beliefs are consistent,
one says that they form an uncertainty equilibrium. One then considers a
two-phase game where the players first choose their attitude and then play the
resulting game. The paper illustrates these notions with a number of games
where the approach provides a new insight into the plausible strategies of the
players.
Bayesian decision theory was created by Leonard Savage. In his "Foundations of Statistics", he says that it would be "preposterous" to use the theory when making decisions in a context in which it is not feasible to fully anticipate all possible pieces of data that may prove relevant in the future. This paper defends Savage's position and considers how Bayesian decision theory might be modified to allow a wider range of legitimate application.