Dan Kovenock

• Chapman University

Strategic decision-making in uncertain and adversarial environments is crucial for the security of modern systems and infrastructures. A salient feature of many optimal decision-making policies is a level of unpredictability, or randomness, which helps to keep an adversary uncertain about the system's defensive strategies. This paper seeks to explo...

Success in adversarial environments often requires investment into additional resources in order to improve one’s competitive position. But, can intentionally decreasing one’s own competitiveness ever provide strategic benefits in such settings? In this paper, we focus on characterizing the role of “concessions” as a component of strategic decision...

In this paper, we highlight scenarios in General Lotto games where there exist incentives to reveal one's intentions to an opponent. The General Lotto game is a popular model of competitive resource allocation. We study a multi-step extension where one player has the option to publicly pre-commit resources to battlefields before play begins. In res...

This article examines the influence of focality in Colonel Blotto games with a lottery contest success function, where the equilibrium is unique and in pure strategies. We hypothesize that the salience of battlefields affects strategic behaviour (the salient target hypothesis) and present a controlled test of this hypothesis against Nash prediction...

In this paper, we generalize the General Lotto game (budget constraints satisfied in expectation) and the Colonel Blotto game (budget constraints hold with probability one) to allow for battlefield valuations that are heterogeneous across battlefields and asymmetric across players and for the players to have asymmetric resource constraints. We comp...

In this paper, we study N-player Colonel Blotto games with incomplete information about battlefield valuations. Such games arise in job markets, research and development, electoral competition, security analysis, and conflict resolution. For M≥N+1 battlefields, we identify a Bayes-Nash equilibrium in which the resource allocation to a given battlef...

Success in adversarial environments often requires investment into additional resources in order to improve one’s competitive position. But, can intentionally decreasing one’s own competitiveness ever provide strategic benefits in such settings? In this paper, we focus on characterizing the role of “concessions” as a component of strategic decision...

Strategic decision-making in uncertain and adversarial environments is crucial for the security of modern systems and infrastructures. A salient feature of many optimal decision-making policies is a level of unpredictability, or randomness, which helps to keep an adversary uncertain about the system’s behavior. This paper seeks to explore decision-...

We consider a class of incomplete-information Colonel Blotto games in which N ≥ 2 agents are engaged in (N + 1) battlefields. An agent's vector of battlefield valuations is drawn from a generalized sphere in Lp-space. We identify a Bayes-Nash equilibrium in which any agent's resource allocation to a given battlefield is strictly monotone in the age...

This paper experimentally examines behavior in a two-player game of attack and defense of a weakest-link network of targets, in which the attacker’s objective is to successfully attack at least one target and the defender’s objective is diametrically opposed. We apply two benchmark contest success functions (CSFs): the auction CSF and the lottery C...

We fully characterize best-response functions in Colonel Blotto games with lottery contest success functions.

We study the two-player, complete information all-pay auction in which a tie ensues if neither player outbids the other by more than a given amount. In the event of a tie, each player receives an identical fraction of the winning prize. Thus players engage in two margins of competition: losing versus tying, and tying versus winning. Two pertinent p...

This article examines behavior in two-person constant-sum Colonel Blotto games in which each player maximizes the expected total value of the battlefields won. A lottery contest success function is employed in each battlefield. Recent experimental research on such games provides only partial support for Nash equilibrium behavior. We hypothesize tha...

In a dynamic contest where it is costly to compete, a player who is behind must decide whether to surrender or to keep fighting in the face of bleak odds. We experimentally examine the game theoretic prediction of last stand behavior in a multi-battle contest with a winning prize and losing penalty, as well as the contrasting prediction of surrende...

In a dynamic contest where it is costly to compete, a player who is behind must decide whether to surrender or to keep fighting in the face of bleak odds. We experimentally examine the game theoretic prediction of last stand behavior in a multi-battle contest with a winning prize and losing penalty, as well as the contrasting prediction of surrende...

Despite the wide occurrence of ties in a variety of contest settings, the strategic interaction that arises when ties are treated as viable outcomes has received little attention. Building on recent theoretical work, we experimentally examine an extension of the canonical two-player all-pay auction in which a tie occurs unless one player’s bid exce...

Maintaining the security of critical infrastructure networks is vital for a modern economy. This paper examines a game-theoretic model of attack and defense of a network in which the defender's objective is to maintain network connectivity and the attacker's objective is to destroy a set of nodes that disconnects the network. The conflict at each n...

In this paper, we generalize the General Lotto game (budget constraints satisfied in expectation) and the Colonel Blotto game (budget constraints hold with probability one) to allow for battlefield valuations that are heterogeneous across battlefields and asymmetric across players, and for the players to have asymmetric resource constraints. We com...

This article examines the impact of the distribution of preferences on equilibrium behavior in conflicts modeled as all-pay auctions with identity-dependent externalities. Centrists and radicals are defined using a willingness-to-pay criterion that admits preferences more general than a simple ordering on the line. Extremism, characterized by a hig...

We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the all-pay auction with complete information and identity-dependent externalities. This condition shows that the generic equilibrium of the standard all-pay auction is robust to the introduction of "small" identity-dependent externalities...

We examine a modified 2 \(\times \) 2 game of Hex in which the winner of each cell is determined by a Tullock contest. The player establishing a winning path of cells in the game wins a fixed prize. Examining the polar cases of all cells being contested simultaneously versus all four cells being contested sequentially, we show that there is an incr...

We derive a necessary and sufficient condition for the existence of equilibria with only two active players in the all-pay auction with complete information and identity-dependent externalities. This condition shows that the generic equilibrium of the standard all-pay auction is robust to the introduction of "small" identity-dependent externalities...

In our original comment, we showed that Hausken’s characterization of Nash equilibrium is invalid for much of the parameter space examined and provided necessary conditions for his solution to hold. Most of the comments in his reply are either tangential or irrelevant. However, several of the claims made in the reply reveal continuing misunderstand...

Many economic, political and social environments can be described as contests in which agents exert costly efforts while competing over the distribution of a scarce resource. These environments have been studied using Tullock contests, all-pay auctions and rank-order tournaments. This survey provides a review of experimental research on these three...

In this article, we examine a model of terrorism that focuses on the tradeoffs facing a terrorist organization that has two qualitatively different attack modes at its disposal. The terrorist organization's objective is to successfully attack at least one target. Success for the target government is defined as defending all targets from any and all...

This article investigates the impact of societal structure on behavior in competitions that can be modeled as all-pay auctions with identity-dependent externalities. The consideration of identity-dependent externalities, which naturally arise in the most common applications of all-pay auctions, enables us to define players' individual characteristi...

We examine a multi-dimensional incomplete information Colonel Blotto game in which each player’s n-tuple of battlefield valuations is drawn from a common n-variate joint distribution function that is uniform on the non-negative orthant of the surface of a sphere.

This article examines a two-stage model of asymmetric conflict based on the classic Colonel Blotto game in which players have, in the first stage, the ability to increase the number of battlefields contested. It thereby endogenizes the "dimensionality" of conflict. In equilibrium, if the asymmetry in the players' resource endowments exceeds a thres...

The Babylonian bridal auction, described by Herodotus, is regarded as one of the earliest uses of an auction in history. Yet, to our knowledge, the literature lacks a formal equilibrium analysis of this auction. We provide such an analysis for the twoplayer case with complete and incompete information, and in so doing identify what we call the "Her...

"We consider the properties of perfectly discriminating contests in which players' abilities are stochastic, but become common knowledge before efforts are expended. Players whose expected ability is lower than that of their rivals may still earn a positive expected payoff from participating in the contest, which may explain why they participate. W...

Hausken (2008a) formulates a contest-theoretic model of the attack and defense of a network of targets. This note identi es a technical error that invalidates Hausken's characterization of Nash equilibrium for a substantial portion of the parameter space that he examines and provides necessary conditions for his solution to form a pure- strategy Na...

Countries compete for new FDI investment, whereas stocks of FDI generate agglomeration benefits and are potentially subject to extortionary taxation. We study the interaction between these aspects in a simple vintage capital framework with discrete time and an infinite horizon, focussing on Markov perfect equilibrium. We show that the equilibrium t...

We study the incentives to share private information ahead of contests, such as markets with promotional competition, procurement contests, or R&D. We consider the cases where firms have (i) independent values and (ii) common values of winning the contest. In both cases, when decisions to share information are made independently, sharing informatio...

This article explores the classic problem of "multiple battlefields," where adversaries allocate resources across different contests, and examines conflicts comprised of component conflicts that are winner-takes-all contests. One of the first games ever formulated, the Colonel Blotto game by Borel in 1921, is an example of such a multi-item contest...

This paper examines a game-theoretic model of attack and defense of multiple networks of targets in which there exist intra-network strategic complementarities among targets. The defender’s objective is to successfully defend all of the networks and the attacker’s objective is to successfully attack at least one network of targets. In this context,...

This paper utilizes a simple model of redistributive politics with voter abstention to analyze the impact of nonpartisan 'get-out-the-vote' efforts on policy outcomes. Although such efforts are often promoted on the grounds that they provide the social benefit of increasing participation in the electoral process, we find that they have a meaningful...

This article examines behavior in the two-player, constant-sum Colonel Blotto game with asymmetric resources in which players maximize the expected number of battlefields won. The experimental results support all major theoretical predictions. In the auction treatment, where winning a battlefield is deterministic, disadvantaged players use a gueril...

In this paper we examine a model of terrorism which focuses on the tradeoffs facing a terrorist organization that has the ability to utilize either or both suicide and conventional terrorism tactics. The terrorist organization's objective is to successfully attack at least one target. Success for the target government is defined as defending all ta...

We study an all-pay contest with multiple identical prizes ("lifeboat seats"). Prizes are partitioned into subsets of prizes ("lifeboats"). Players play a two-stage game. First, each player chooses an element of the partition ("a lifeboat"). Then each player competes for a prize in the subset chosen ("a seat"). We characterize and compare the subga...

This paper presents a unified framework for characterizing symmetric equilibrium in simultaneous move, two-player, rank-order contests with complete information, in which each player’s strategy generates direct or indirect affine “spillover” effects that depend on the rank-order of her decision variable. These effects arise in natural interpretatio...

The formation of an alliance in conflict situations is known to suffer from a collective action problem and from the potential of internal conflict. We show that budget constraints of an intermediate size can overcome this strong disadvantage and explain the formation of alliances.

Countries compete for new FDI investment, whereas stocks of FDI generate agglomeration benefits and are potentially subject to extortionary taxation. We study the interaction between these aspects in a simple vintage capital framework with discrete time and an infinite horizon, focussing on Markov perfect equilibrium. We show that the equilibrium t...

In 2005, the Democratic National Committee adopted the 50-state strategy in lieu of the strategy of focusing solely on battleground states. The rationale given for this move is that campaign expenditures are durable outlays that impact both current and future campaigns. This paper investigates the optimality of the 50-state strategy in a simple dyn...

This article presents the classic Bertrand model of oligopolistic price competition and shows how alternative assumptions on economic primitives – such as the structure of demand and cost functions, tie-breaking rules, and product differentiation – shape Nash equilibrium prices and profits. We also discuss the related Bertrand–Edgeworth model of pr...

This paper examines the effect of inefficient redistribution in Myerson’s (1993) model of redistributive politics. Regardless of the absolute levels of the efficiency of political parties’ transfers to different voter segments, parties have incentive to (stochastically) shift resources away from voter segments with large relative efficiency gaps be...

This paper examines a multi-player and multi-front Colonel Blotto game in which one player, A, simultaneously competes in two disjoint Colonel Blotto games, against two separate opponents, 1 and 2. Prior to competing in the games, players 1 and 2 have the opportunity to form an alliance to share their endowments of a one-dimensional resource (e.g.,...

We consider the properties of perfectly discriminating contests in which players' abilities are stochastic, but become common knowledge before efforts are expended. Players whose expected ability is lower than that of their rivals may still earn a positive expected payoff from participating in the contest, which may explain why they participate. We...

We study equilibrium in a multistage race in which players compete in a sequence of simultaneous move component contests. Players may win a prize for winning each component contest, as well as a prize for winning the overall race. Each component contest is an all-pay auction with complete information. We characterize the unique subgame perfect equi...

This article studies electoral competition in a model of redistributive politics with deterministic voting and heterogeneous voter loyalties to political parties. We construct a natural measure of 'party strength' based on the sizes and intensities of a party's loyal voter segments and demonstrate how party behavior varies with the two parties' str...

We examine free riding and underinvestment in noncooperative entry deterrence in the Gilbert and Vives (1986) model with differentiated products. Our analysis proves that for products that are differentiated enough, when both entry allowing and entry deterring equilibria coexist, the symmetric entry deterring equilibrium may Pareto dominate the ent...

This paper contributes to the study of tacit collusion by analyzing infinitely repeated multiunit uniform price auctions in a symmetric oligopoly with capacity constrained firms. Under both the Market Clearing and Maximum Accepted Price rules of determining the uniform price, we show that when each firm sets a price-quantity pair specifying the fir...

We examine free riding and underinvestment in noncooperative entry deterrence in the Gilbert and Vives (1986) model with differentiated products. Our analysis proves that for products that are differentiated enough, when both entry allowing and entry deterring equilibria coexist, the symmetric entry deterring equilibrium may Pareto dominate the ent...

A simple auction-theoretic framework is used to examine symmetric litigation environments where the legal ownership of a disputed asset is unknown to the court. The court observes only the quality of the case presented by each party, and awards the asset to the party presenting the best case. Rational litigants influence the quality of their cases...

We characterize the unique Markov perfect equilibrium of a tug-of-war without exogenous noise, in which players have the opportunity to engage in a sequence of battles in an attempt to win the war. Each battle is an all-pay auction in which the player expending the greater resources wins. In equilibrium, contest effort concentrates on at most two a...

In an article published in this journal, Rapoport and Amaldoss (2000, Journal of Economic Behavior and Organization, 42, 483-521) analyze symmetric and asymmetric investment games similar to two-player all-pay auctions with bid caps. In this note, we correct an error in their characterization of the set of Nash Equilibria of their symmetric investm...

In this note, we characterize the full set of Equilibria of the 2-firm patent race analyzed by Amaldoss and Jain (Management Science, 48(8), August 2002, pp. 972-991). Contrary to Amaldoss and Jain’s (2002) claim, we show that the equilibrium is not always unique and that the set of Equilibria is non-robust to changes in the (discrete) set of avail...

This paper examines the feasibility of collusion in capacity constrained duopoly supergames. In each period firms simultaneously set a price-quantity pair specifying the price for the period and the maximum quantity the firm is willing to sell as this price. Under price-quantity competition firms are able to ration their output below capacity. For...

This article examines the properties of independent-private-value all-pay and winner-pay auctions when there are multiple units sold. We study bidding behavior, efficiency, and revenue in a set of 23 experimental sessions. Our data show that the all-pay auction and the winner-pay auction are empirically revenue equivalent, though both yield higher...

The state of the art of rendering fiat money valuable is either to impose a boundary condition or to make the boundary condition unimportant through an infinite sequence of markets so as to circumvent backward induction. We show fiat exchange may nevertheless arise in finite economies if agents have incomplete information about their relative posit...

This chapter utilizes the results of Deneckere ·& Kovenock (1988, 1989, 1992, 1996) on price setting games with capacity constraints and different unit costs up to capacity to analyze the effects of quotas and tariffs in a model in which a domestic market for a homogeneous product is supplied by a duopoly consisting of a domestic and a foreign firm...

"A simple action-theoretic framework is used to examine symmetric litigation environments where the legal ownership of a disputed asset is unknown by the court. The court observes only the quality of the case presented by each party, and awards the asset to the party presenting the best case. Rational litigants influence the quality of their cases...

With few exceptions, the literature on the role of capacity as a strategic entry deterrent has assumed Cournot competition in the post-entry game. In contrast, this paper studies a model in which the incumbent and entrant sequentially precommit to capacity levels before competing in price. Interesting deterrence effects arise because firms need tim...

Tullock's analysis of rent seeking and overdissipation is reconsidered. We show that, while equilibrium strategies do not permit overdissipation in expectation, for particular realizations of players' mixed strategies the total amount spent competing for rents can exceed the value of the prize. We also show that the cross-sectional incidence of ove...

Gordon Tullock's analysis of rent seeking and overdissipation is reconsidered. The authors show that, while equilibrium strategies do not permit overdissipation in expectation, for particular realizations of players' mixed strategies the total amount spent competing for rents can exceed the value of the prize. They also show that the cross-sectiona...

This paper extends the analysis of the n-player all-pay auction with complete information to cover the case of m≤n prizes, valued in weakly decreasing order, but symmetrically across players. We provide a complete characterization of the Nash equilibrium distributions for this class of auctions and provide an exact expression for the expected reven...

We examine the implications of replacing the Cournot market clearing assumption with Bertrand-Edgeworth behavior when production is time-consuming. The benchmark is Saloner's result that when two firms simultaneously choose quantities in each of two periods before the market clears, every point on the outer envelope of the reaction functions betwee...

We examine whether sharp debt increases through leveraged buyouts and recapitalizations interact with market structure to influence plant closing and investment decisions of recapitalizing firms and their rivals. We take into account the fact that recapitalizations and investment decisions are both endogenous and may be simultaneously influenced by...

In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show t...

This paper characterizes the set of Nash equilibria in a price setting duopoly in which firms have limited capacity, and in which unit costs of production up to capacity may differ. Assuming concave revenue and efficient rationing, we show that the case of different unit costs involves a tractable generalization of the methods used to analyze the c...

In a (first price) all-pay auction, bidders simultaneously submit bids for an item. All players forfeit their bids, and the high bidder receives the item. This auction is widely used in economics to model rent seeking, R&D races, political contests, and job promotion tournaments. We fully characterize equilibrium for this class of games, and show t...

This paper presents empirical evidence on the interaction of capital structure decisions and product market behavior. We examine when firms recapitalize and increase the proportion of debt in their capital structure. The evidence in this paper shows that firms with low productivity plants in highly concentrated industries are more likely to recapit...

This paper models localized competition between firms when there is consumer lock-in or loyalty. We derive the symmetric equilibrium mixed strategy price distribution under two alternative models, and compare them to symmetric equilibrium strategies under non-localized competition. Contrary to the conventional wisdom in the product differentiation...

I modify the uniform-price auction rules in allowing the seller to ration bidders. This allows me to provide a strategic foundation for underpricing when the seller has an interest in ownership dispersion. Moreover, many of the so-called "collusive-seeming" equilibria disappear.

This paper characterizes the set of NASH equilibria in a price setting duopoly in which firms have limited capacity, and in which unit costs of production up to capacity may differ. Assuming concave revenue and efficient rationing, we show that the case of different unit costs involves a tractable generalization of the methods used to analyze the c...

With few exceptions, the literature on the role of capacity as a strategic entry deterrent has assumed Cournot competition in the post-entry game. In contrast, our model is in the spirit of Kreps and Scheinkman (1983): the incumbent and entrant sequentially precommit to capacity levels before competing in price. Interesting deterrence effects arise...

In G. Tullock's rent-seeking model, the probability that a player wins the game depends on expenditures raised to the power R. The authors show that a symmetric mixed-strategy Nash equilibrium exists when R "is greater than" 2, and that overdissipation of rents does not arise in any Nash equilibrium. The authors derive a tight bound on the level of...

In this paper, we investigate project selection choices of duopolists facing two alternatives: undertaking a "pioneering" type project (Type A) aimed to develop a highly innovative product, or an "incremental innovation" type project (Type B) aimed to develop a less innovative product such as the modification of an existing product. A key objective...

This paper analyzes Stackelberg price leadership in a duopoly in which firms are capacity constrained and products are imperfect substitutes. Assuming symmetric substitutes, linear demand, and efficient rationing, we characterize the equilibria with an exogenously specified leader. Using the equilibrium profits derived from these games, we argue th...

In Tullock’s rent-seeking model, the probability a player wins the game depends on expenditures raised to the power R. We show that a symmetric mixed-strategy Nash equilibrium exists when R > 2, and that overdissipation of rents does not arise in any Nash equilibrium. We derive a tight lower bound on the level of rent dissipation that arises in a s...

We show that the Varian model of sales with more than two firms has two types of equilibria: a unique symmetric equilibrium, and a continuum of asymmetric equilibria. In contrast, the 2-firm game has a unique equilibrium that is symmetric. For the n-firm case the asymmetric equilibria imply mixed strategies that can be ranked by first-order stochas...

This paper analyzes GATT and its dispute settlement procedure (DSP) in the context of a supergame model of international trade featuring both explicit and implicit agreements. An explicit agreement, such as GATT, may be violated at some positive cost in addition to retaliatory actions that might be induced by the violation. We interpret this cost a...

This paper examines the profitability of running an advertisement that promises to pay damages to customers who can find a (serious) price offer that the firm will not undercut. We show that such an advertisement can support a collusive price, and furthermore, that no other firm has an incentive to duplicate the advertisement. The results are shown...

This paper analyzes a duopolistic price setting game in which firms have loyal consumer segments but cannot distinguish them from price-sensitive consumers. The authors adapt a variant of H. Varian's (1980) simultaneous price setting game to analyze price-leader equilibria. The properties of the price-leader equilibria with an exogenously specified...

This paper analyzes duopolistic price-leadership games in which firms have capacity constraints. We provide a complete characterization of price leader equilibria under quite general assumptions on demand and for arbitrary capacities. We show that when capacities are in the range where the simultaneous-move price-setting game (with efficiently rati...

In this paper we present a simple price leadership model in which equilibrium behavior exhibits price rigidity following downward demand shocks and price flexibility after an upturn in demand. The source of this asymmetric rigidity lies in the fact that leader-follower equilibrium prices are lower than their collusive levels and that any firm leadi...

This paper presents a simple model of sequential wage setting by two unions, each of which is attached to a firm in a duopolistic output market. We find that for a large range of unanticipated downward demand shocks, the equilibrium exhibits downward wage rigidity. Neither union chooses to alter its wage even though wages are flexible. This occurs...

This paper analyzes employee stock ownership plans in an implicit contract model under asymmetric information. Our model assumes that worker compensation schemes involve wage and stock payments, or wage-share contracts, and treats shares of stock as an enforceable claim on the firm's realized profits. In this setting, we show conditions under which...

In this paper, collusive price leadership in homogeneous good capacity-constrained repeated price competition is examined. In the stage game, firms choose their timing of price setting. Although setting a price early is disadvantageous per se, a large firm has an incentive to move early in order to demonstrate its commitment not to deviate. If the...

In this paper we explore the determination of the sequencing of wage bargains in an institutional structure consisting of a single firm employing two unions, under two alternative assumptions about the nature of feasible contracts. If contingent contracts are prohibitively costly, we find that the unions prefer to lead in the negotiations process i...

In this article we examine the effect of private information and information externalties on the ex post efficiency of investment in oil exploration. We show that too much drilling tends to occur if firms believe that the area is likely to contain a sizeable pool of oil, and too little drilling occurs if the opposite is true. Bargaining with well-d...