Games Econ Research Articles

Average tree solutions and the distribution of Harsanyi dividends

We consider communication situations games being the combination of a TU-game and a communication graph. We study the average tree (AT) solutions introduced by Herings et al. (Games Econ Behav 62:77–92, 2008; Games Econ Behav 68:626–633, 2010). The AT solutions are defined with respect to a set, say $${\fancyscript{T}}$$ , of rooted spanning trees of the communication graph. We prove the following results. Firstly, the AT solution with respect to $${\fancyscript{T}}$$ is a Harsanyi solution if and only if $${\fancyscript{T}}$$ is a subset of the set of trees introduced in Herings et al. (2010). Secondly, the latter set is constructed by the classical DFS algorithm and the associated AT solution coincides with the Shapley value when the communication graph is complete. Thirdly, the AT solution with respect to trees constructed by the other classical algorithm BFS yields the equal surplus division when the communication graph is complete.

Hospital’s activity-based financing system and manager: physician interaction

This paper examines the consequences of the introduction of an activity-based reimbursement system on the behavior of physicians and hospital's managers. We consider a private for-profit sector where both hospitals and physicians are initially paid on a fee-for-service basis. We show that the benefit of the introduction of an activity-based system depends on the type of interaction between managers and physicians (simultaneous or sequential decision-making games). It is shown that, under the activity-based system, a sequential interaction with physician leader could be beneficial for both agents in the private sector. We further model an endogenous timing game à la Hamilton and Slutsky (Games Econ Behav 2: 29-46, 1990) in which the type of interaction is determined endogenously. We show that, under the activity-based system, the sequential interaction with physician leader is the unique subgame perfect equilibrium.

An improved algorithm for detecting potential games

This note presents a simple necessary and sufficient condition for a game to be a potential game. My condition improves on the well-known condition in Monderer and Shapley (Games Econ Behav 14:124–143, 1996) in the sense that it leads to a significant reduction in the computational burden in determining whether a given game is a potential game. It also provides a logical connection between finite and continuous potential games, as it can be understood as a faithful translation of one type of characterization for a continuous potential game.

The multichoice coalition value

In this paper we define a solution for multichoice games which is a generalization of the Owen coalition value (Lecture Notes in Economics and Mathematical Systems: Essays in Honor of Oskar Morgenstern, Springer, New York, pp. 76–88, 1977) for transferable utility cooperative games and the Egalitarian solution (Peters and Zanks, Ann. Oper. Res. 137, 399–409, 2005) for multichoice games. We also prove that this solution can be seen as a generalization of the configuration value and the dual configuration value (Albizuri et al., Games Econ. Behav. 57, 1–17, 2006) for transferable utility cooperative games.

Attribution and reciprocity

Abstract People infer causes and assign responsibilities for situations they find themselves in. In contradiction with classical presumptions about human behavior, it has been found that the assignment of responsibilities influences people's perceptions about the (un)kindness of others. Kindness perceptions, in turn, influence behavior. Dufwenberg and Kirchsteiger [Dufwenberg, M., Kirchsteiger, G., 2004. A theory of sequential reciprocity. Games Econ. Behav. 47 (2), 268–298] formalize this empirical finding in their ‘theory of sequential reciprocity’. This paper extends their analysis by moves of chance. More precisely, an extended framework is presented which allows for the analysis of strategic interactions of reciprocal agents in situations in which material outcomes also depend on chance. Moves of chance influence the attribution of responsibilities, people's perceptions about the (un)kindness of others and, hence, their reciprocal behavior. Furthermore, with the help of two applications it is demonstrated how this framework can be used to explain experimental findings showing that people react very differently in outcomewise-identical situations depending on the moves of chance involved.

Risk aversion and expected utility of consumption over time

The calibration theorem by Rabin [Rabin, M., 2000a. Risk aversion and expected utility theory: A calibration theorem. Econometrica 68, 1281-1292; Rabin, M., 2000b. Diminishing marginal utility of wealth cannot explain risk aversion. In: Kahneman, D., Tversky, A. (Eds.), Choices, Values and Frames. Cambridge University Press] implies that seemingly plausible small-stake choices under risk imply implausible large-stake risk aversion. This theorem is derived based on the expected utility of wealth model. However, Cox and Sadiraj [Cox, J.C., Sadiraj, V., 2006. Small- and large-stakes risk aversion: Implications of concavity calibration for decision theory. Games Econ. Behav. 56, 45-60] show that such implications do not follow from the expected utility of income model. One may then wonder about the implications for more applied consumption analysis. The present paper therefore expresses utility as a function of consumption in a standard life cycle model, and illustrates the implications of this model with experimental small- and intermediate-stake risk data from Holt and Laury [Holt, C.A., Laury, S.K., 2002. Risk aversion and incentive effects. Amer. Econ. Rev. 92, 1644-1655]. The results suggest implausible risk aversion parameters as well as unreasonable implications for long-term risky choices. Thus, the conventional intertemporal consumption model under risk appears to be inconsistent with the data. (C) 2009 Elsevier Inc. All rights reserved. (Less)

Polytopes and the existence of approximate equilibria in discontinuous games

Radzik [Radzik, T., 1991. Pure-strategy ε-Nash equilibrium in two-person non-zero-sum games. Games Econ. Behav. 3, 356–367] showed that, by strengthening the usual quasi-concavity assumption on players' payoff functions, upper semi-continuous two-player games on compact intervals of the real line have ε-equilibria for all ε > 0 . Ziad [Ziad, A., 1997. Pure-strategy ε-Nash equilibrium in n-person nonzero-sum discontinuous games. Games Econ. Behav. 20, 238–249] then stated that the same conclusion holds for n-player games on compact, convex subsets of R m , m ⩾ 1 , provided that the upper semi-continuity condition is strengthened. Both Radzik's and Ziad's proofs rely crucially on the lower hemi-continuity of the ε-best reply correspondence. We show that: (1) in contrast to what is stated by Ziad, his conditions fail to be sufficient for the lower hemi-continuity of the approximate best-reply correspondence, (2) the approximate best-reply correspondence is indeed lower hemi-continuous if players' action spaces are polytopes, and (3) with action spaces as polytopes, Ziad's theorem can be stated so that it properly generalizes Radzik's theorem.

Truth and trust in communication: Experiments on the effect of a competitive context

The paper analyses the results of a Communication Game in a cooperative or a competitive context. In this game, decision makers face uncertainty about the consequences of their choice, but can rely on recommendations from advisors. Financial incentives between alternatives are not aligned for the two players, which produces an incentive to lie. While many advisors tell the truth against their monetary self-interest, the propensity to tell the truth is unaffected by the contextual variation. In contrast, decision makers show less trust in a competitive context, but only when they have no explicit information about the payoff alignment. The context seems to shape their belief about the situation. The data of this study is largely in line with Subjective Equilibrium Analysis [Kalai, E., Lehrer, E., 1995. Subjective games and equilibria. Games Econ. Behav. 8 (1), 123–163].

Coasian dynamics in repeated English auctions

We extend the Coase conjecture to the case of a seller with a single object, who faces n potential buyers and holds a sequence of English auctions until the object is sold. In an independent-private-values environment in which buyers and sellers share the same discount factor, we show that the (perfect Bayesian) equilibrium path of reserve prices obeys a Coasian logic. Moreover, the equilibrium reserve path lies below that for the repeated sealed-bid, second-price auctions studied by McAfee and Vincent (in Games Econ Behav 18:246–276). Nevertheless, the open (English) and sealed-bid formats are shown to be revenue equivalent.

Strategic Aspects of the 1995 and 2004 EU Enlargements

While the 1995 entrants to the EU are by now fully integrated, those joining in 2004 still “enjoy” a secondary status for a number of years. We attribute this difference to the fact that unlike the former EFTA members joining in 1995, the 2004 entrants formed a group with heterogenous interests, one that lacked the same strong internal economic ties. Not being able to act as a unified block they had a considerably weaker bargaining position. We support our arguments by qualitative results from a simple model, a dynamic partition function game based on Yi (Games Econ Behav 20:201–237, 1997) and Morelli and Penelle (Economic integration as a partition function game 1997).

Payoff dominance and risk dominance in the observable delay game: a note

We examine whether the payoff dominant sequential-move (Stackelberg) outcome is realized when timing is endogenized. We adopt the observable delay game formulated by Hamilton and Slutsky [Games Econ Behav 2(1):29–46, 1990]. We find that if one sequential-move outcome is payoff dominant, either (i) the outcome both players prefer is the unique equilibrium; or (ii) two sequential-move outcomes are equilibria and the one both players prefer is risk dominant. In other words, no conflict between payoff dominance and risk dominance in the observable delay game exists, in contrast to other games such as (non pure) coordination games. We also find that even if one of two sequential-move outcomes is the unique equilibrium outcome in the observable delay game, it does not imply that the equilibrium outcome is payoff dominant to the other sequential-move outcome.

On cooperative games with large monotonic core

Cooperative games with large core were introduced by Sharkey (Int. J. Game Theory 11:175–182, 1982), and the concept of Population Monotonic Allocation Scheme was defined by Sprumont (Games Econ. Behav. 2:378–394, 1990). Inspired by these two concepts, Moulin (Int. J. Game Theory 19:219–232, 1990) introduced the notion of large monotonic core giving a characterization for three-player games. In this paper we prove that all games with large monotonic core are convex. We give an effective criterion to determine whether a game has a large monotonic core and, as a consequence, we obtain a characterization for the four-player case.

The cutting power of preparation

In a strategic game, a curb set (Basu and Weibull, Econ Lett 36:141–146, 1991) is a product set of pure strategies containing all best responses to every possible belief restricted to this set. Prep sets (Voorneveld, Games Econ Behav 48:403–414, 2004) relax this condition by only requiring the presence of at least one best response to such a belief. The purpose of this paper is to provide sufficient conditions under which minimal prep sets give sharp predictions. These conditions are satisfied in many economically relevant classes of games, including supermodular games, potential games, and congestion games with player-specific payoffs. In these classes, minimal curb sets generically have a large cutting power as well, although it is shown that there are relevant subclasses of coordination games and congestion games where minimal curb sets have no cutting power at all and simply consist of the entire strategy space.

Spoilers, blocking coalitions, and the core

This paper surveys non-cooperative implementations of the core which tell an intuitive story of coalition formation. Under the core solution concept, if a blocking coalition exists those agents abandon the current allocation without regard for the consequences to players outside the blocking coalition. Yet in certain circumstances, these players have an incentive to prevent formation of any blocking coalition; a game analyzed in Lagunoff (Games Econ Behav 7:54–61, 1994) is vulnerable to such circumstances. To obtain all core allocations and only core allocations, a mechanism must either restrict the actions of non-members of a proposed coalition, or ensure that non-members are unharmed by the departure of the coalition. These requirements illustrate the core’s nonchalance toward agents not in blocking coalitions.

Equivalence theorem, consistency and axiomatizations of a multi-choice value

This paper is devoted to the study of solutions for multi-choice games which admit a potential, such as the potential associated with the extended Shapley value proposed by Hsiao and Raghavan (Int J Game Theory 21:301---302, 1992; Games Econ Behav 5:240---256, 1993). Several axiomatizations of the family of all solutions that admit a potential are offered and, as a main result, it is shown that each of these solutions can be obtained by applying the extended Shapley value to an appropriately modified game. In the framework of multi-choice games, we also provide an extension of the reduced game introduced by Hart and Mas-Colell (Econometrica 57:589---614, 1989). Different from the works of Hsiao and Raghavan (1992, 1993), we provide two types of axiomatizations, one is the analogue of Myerson's (Int J Game Theory 9:169---182, 1980) axiomatization of the Shapley value based on the property of balanced contributions. The other axiomatization is obtained by means of the property of consistency.

Population monotonic path schemes for simple games

A path scheme for a game is composed of a path, i.e., a sequence of coalitions that is formed during the coalition formation process and a scheme, i.e., a payoff vector for each coalition in the path. A path scheme is called population monotonic if a player’s payoff does not decrease as the path coalition grows. In this study, we focus on Shapley path schemes of simple games in which for every path coalition the Shapley value of the associated subgame provides the allocation at hand. Obviously, each Shapley path scheme of a game is population monotonic if and only if the Shapley allocation scheme of the game is population monotonic in the sense of Sprumont (Games Econ Behav 2:378–394, 1990). We prove that a simple game allows for population monotonic Shapley path schemes if and only if the game is balanced. Moreover, the Shapley path scheme of a specific path is population monotonic if and only if the first winning coalition that is formed along the path contains every minimal winning coalition. We also show that each Shapley path scheme of a simple game is population monotonic if and only if the set of veto players of the game is a winning coalition. Extensions of these results to other efficient probabilistic values are discussed.

Note on universal conditional consistency

This note clarifies the implication of universal conditional consistency (UCC) in Fudenberg and Levine (Games Econ Behav 29:104–130, 1999) from the viewpoint of the no-regret test. We first show that the UCC property implies (universally) passing any countable set of no-regret tests. Furthermore, we show that the UCC implies universally passing uncountable (particular) no-regret tests so that the UCC theorem and the wide-range no-regret (WRNR) theorem in Lehrer (Games Econ Behav 42:101–115, 2003) may differ, as opposed to the thought that the UCC property is a special case of the WRNR property.

A general structure theorem for the Nash equilibrium correspondence

I consider n-person normal form games where the strategy set of each player is a non-empty compact convex subset of an Euclidean space, and the payoff function of player i is continuous in joint strategies and continuously differentiable and concave in the player i's strategy. No further restrictions (such as multilinearity of the payoff functions or the requirement that the strategy sets be polyhedral) are imposed. I demonstrate that the graph of the Nash equilibrium correspondence on this domain is homeomorphic to the space of games. This result generalizes a well-known structure theorem in [Kohlberg, E., Mertens, J.-F., 1986. On the strategic stability of equilibria. Econometrica 54, 1003–1037]. It is supplemented by an extension analogous to the unknottedness theorems in [Demichelis S., Germano, F., 2000. Some consequences of the unknottedness of the Walras correspondence. J. Math. Econ. 34, 537–545; Demichelis S., Germano, F., 2002. On (un)knots and dynamics in games. Games Econ. Behav. 41, 46–60]: the graph of the Nash equilibrium correspondence is ambient isotopic to a trivial copy of the space of games.

Inequality averse multi-utilitarian bargaining solutions

This paper introduces and analyzes the class of inequality averse multi-utilitarian solutions for cooperative bargaining problems. We show that generalized Gini solutions and inequality averse Choquet solutions are particular cases of this new multi-valued solution concept and provide a complete characterization in which an invariance property, consisting of a weakening of both the linear invariance axiom in Blackorby et al. (Econometrica 62:1161–1178, 1994) and the restricted invariance axiom in Ok and Zhou (Games Econ Behav 33:249–264, 2000), plays an important role. Moreover, by relaxing the assumptions involved in the characterization, the class is extended to include inequality loving multi-utilitarian solutions which are also studied in the paper.

Sequential equilibrium in monotone games: A theory-based analysis of experimental data

A monotone game is an extensive-form game with complete information, simultaneous moves and an irreversibility structure on strategies. It captures a variety of situations in which players make partial commitments and allows us to characterize conditions under which equilibria result in socially desirable outcomes. However, since the game has many equilibrium outcomes, the theory lacks predictive power. To produce stronger predictions, one can restrict attention to the set of sequential equilibria, or Markov equilibria, or symmetric equilibria, or pure-strategy equilibria. This paper explores the relationship between equilibrium behavior in a class of monotone games, namely voluntary contribution games, and the behavior of human subjects in an experimental setting. Several key features of the symmetric Markov perfect equilibrium (SMPE) are consistent with the data. To judge how well the SMPE fits the data, we estimate a model of Quantal Response Equilibrium (QRE) [R. McKelvey, T. Palfrey, Quantal response equilibria for normal form games, Games Econ. Behav. 10 (1995) 6–38; R. McKelvey, T. Palfrey, Quantal response equilibria for extensive form games, Exp. Econ. 1 (1998) 9–41] and find that the decision rules of the QRE model are qualitatively very similar to the empirical choice probabilities.