Testing theories of behavior for extensive-form two-player two-stage games

We examine choices in two-player extensive-form games that give subjects opportunities for individualistic as well as other-regarding behavior, and where each subject makes choices in a variety of games. Following an extensive search over models, where we estimate a single parameter vector for all the games rather than different parameter vectors for each game, we find that (1) the level-n model organizes the data well, (2) other-regarding behaviors in these games appear to consist primarily of egalitarian and utilitarian behaviors, and (3) there is no significant evidence for reciprocal behavior. Electronic Supplementary Material  The online version of this article () contains supplementary material, which is available to authorized users.     

Fending off one means fending off all: evolutionary stability in quasi-submodular aggregative games

The implications of evolutionarily stable behavior in finite populations have recently been explored for a variety of aggregative games. This note proves an intimate relationship between quasi-submodularity and global evolutionary stability of strategies for these games, which – apart from being of independent interest – accounts for a number of results obtained in the recent literature: we show that any evolutionarily stable strategy of a quasi-submodular aggregative game must also be globally stable. That is, if one mutant cannot successfully invade a population, any number of mutants can do so even lessThe author is grateful to Ana Ania and Carlos Alōs-Ferrer for comments on an earlier version     

Dynamic unawareness and rationalizable behavior

We define generalized extensive-form games which allow for asymmetric awareness of actions. We extend Pearceʼs (1984) notion of extensive-form (correlated) rationalizability to this setting, explore its properties, and prove existence.     

Evolutionary economics goes mainstream: A review of the theory of learning in games

The Theory of Learning in Games by Fudenberg and Levine surveys a key branch of evolutionary economics from a mainstream perspective. Its publication provides an opportunity to reassess the prospects and goals for evolutionary economics.     

On economic applications of evolutionary game theory

Evolutionary games have considerable unrealized potential for modeling substantive economic issues. They promise richer predictions than orthodox game models but often require more extensive specifications. This paper exposits the specification of evolutionary game models and classifies the possible asymptotic behavior for one and two dimensional models.     

Asymmetric evolutionary games with non-linear pure strategy payoffs

In this paper, I extend the analytical framework of evolutionary game theory to games with two distinct types of players where the type-specific payoff functions are nonlinear on the right—bi-player-type nonlinear (BNL) evolutionary games. That is, asymmetric games where the payoffs for pairwise interactions are influenced by the ambient frequencies of the pertinent strategies of both types of players.While this paper is motivated by my interest in inter- and intra-gender conflicts of interest in sexual reproduction, BNL games also arise just as naturally in most two-species interactions. Thus, the methodology may provide a novel approach to investigating such classical ecological phenomena as prey–predator/host–parasite interactions and interspecies competition for resources.Finally, given the growing tendency to utilize evolutionary games in economic modeling, a case can be made for the current paper being of interest to traditional game-theoretic modelers in connection with situations such as buyer/seller or employer/employee interaction.     

The evolution of conventions in minimum effort games

The literature on minimum effort game has been concerned with a symmetric game with linear payoff functions. The main aim of the present paper is to study the coordination problem arising in a not necessarily symmetric minimum effort game with two players. The sources of asymmetry can be twofold: the productivity of effort and the distribution of the join output. To select among the Pareto ranked equilibria we use the stochastic stability criterion. We show that, for any configuration parameters, the set of stochastically stable equilibria coincides with the set of potential maximizers. We also show that when the disutility of effort is linear, the Pareto dominant equilibrium is stochastically stable provided that the distributive parameter belongs to a well defined range. When the disutility of effort is nonlinear no distributive arguments can be used to successfully affect the selection process. Lastly we prove that the connection between stochastic stability and maximum potential can fail when more than two agents are considered.     

Cycling in a stochastic learning algorithm for normal form games

In this paper we study a stochastic learning model for 2×2 normal form games that are played repeatedly. The main emphasis is put on the emergence of cycles. We assume that the players have neither information about the payoff matrix of their opponent nor about their own. At every round each player can only observe his or her action and the payoff he or she receives. We prove that the learning algorithm, which is modeled by an urn scheme proposed by Arthur (1993), leads with positive probability to a cycling of strategy profiles if the game has a mixed Nash equilibrium. In case there are strict Nash equilibria, the learning process converges a.s. to the set of Nash equilibria.     

Coalition formation in general apex games under monotonic power indices

An apex game consists of one apex player and a set of minor players. We identify two key properties of apex games and use them to introduce the class of general apex games. We derive players' preferences over winning coalitions by applying strongly monotonic power indices on such a game and all its subgames and investigate whether there are core stable coalitions in the induced hedonic coalition formation game. Besides several general results, in particular, we develop conditions on the game for the Shapley–Shubik index, the Banzhaf index, and the normalized Banzhaf index.     

A note on control costs and logit rules for strategic games

We consider best response dynamics with endogenous noise based on a finite game in strategic form. A player can reduce the noise level by expending an extra effort and incurring some disutility or control costs. We specify control costs that result in logit adjustment rules. The stochastically stable states of the dynamic process are partial Nash configurations, that is, states where at least one player plays a best response against the others. If the game has a potential, then the stochastically stable states coincide with the Nash equilibria on which the potential is maximized. RID="*" ID="*" Instructive comments of a referee are gratefully acknowledged. Correspondence to:H. Haller     

Large newsvendor games

We consider a game, called newsvendor game, where several retailers, who face a random demand, can pool their resources and build a centralized inventory that stocks a single item on their behalf. Profits have to be allocated in a way that is advantageous to all the retailers. A game in characteristic form is obtained by assigning to each coalition its optimal expected profit. We consider newsvendor games with possibly an infinite number of newsvendors. We prove in great generality results about balancedness of the game, and we show that in a game with a continuum of players, under a nonatomic condition on the demand, the core is a singleton. For a particular class of demands we show how the core shrinks to a singleton when the number of players increases.     

Brown–von Neumann–Nash dynamics: The continuous strategy case

Brown and von Neumann introduced a dynamical system that converges to saddle points of zero sum games with finitely many strategies. Nash used the mapping underlying these dynamics to prove existence of equilibria in general games. The resulting Brown–von Neumann–Nash dynamics are a benchmark example for myopic adjustment dynamics that, in contrast to replicator dynamics, allow for innovation, but require less rationality than the best response dynamics. This paper studies the BNN dynamics for games with infinitely many strategies. We establish Nash stationarity for continuous payoff functions. For negative semidefinite games (that include zero sum games), we generalize the results of Brown and von Neumann. In addition, we show that evolutionarily robust Nash equilibria are asymptotically stable. A complete stability analysis for doubly symmetric games is also obtained.     

Repeated signaling games

I analyze a class of repeated signaling games in which the informed player's type is persistent and the history of actions is perfectly observable. In this context, a large class of possibly complex sequences of signals can be supported as the separating equilibrium actions of the “strong type” of the informed player. I characterize the set of such sequences. I also characterize the sequences of signals in least cost separating equilibria (LCSE) of these games. In doing this, I introduce a state variable that can be interpreted as a measure of reputation. This gives the optimization problem characterizing the LCSE a recursive structure. I show that, in general, the equilibrium path sequences of signals have a simple structure. The shapes of the optimal sequences depend critically on the relative concavities of the payoff functions of different types, which measure the relative preferences towards payoff smoothing.     

Evolution in games with a continuous action space

Allowing for games with a continuous action space, we investigate how evolutionary stability, the existence of a uniform invasion barrier, local superiority and asymptotic stability relate to each other. This is done without restricting the populations of which we want to investigate the stability to monomorphic population states or to strategies with finite support. The authors have benefitted from careful and precise comments by Gerard van der Laan, Jan van Mill, the editor and an anonymous referee. Matthijs van Veelen gratefully acknowledges financial support by the Netherlands’ Organization for Scientific Research (NWO).     

On the Dynamic Foundation of Evolutionary Stability in Continuous Models

We show in this paper that none of the existing static evolutionary stability concepts (ESS, CSS, uninvadability, NIS) is sufficient to guarantee dynamic stability in the weak topology with respect to standard evolutionary dynamics if the strategy space is continuous. We propose a new concept, evolutionary robustness, which is stronger than the previous concepts. Evolutionary robustness ensures dynamic stability for replicator dynamics in doubly symmetric games. Journal of Economic Literature Classification Numbers: C70, 72.     

Learning with bounded memory in games

We study learning with bounded memory in zero-sum repeated games with one-sided incomplete information. The uninformed player has only a fixed number of memory states available. His strategy is to choose a transition rule from state to state, and an action rule, which is a map from each memory state to the set of actions. We show that the equilibrium transition rule involves randomization only in the intermediate memory states. Such randomization, or less frequent updating, is interpreted as a way of testing the opponent, which generates inertia in the player's behavior and is the main short-run bias in information processing exhibited by the bounded memory player.     

Interconnected games and international environmental problems

The purpose of this paper is to introduce the concept of interconnected games and to show its relevance for modeling international environmental problems. It is argued that an interconnected game approach to international environmental problems may enhance cooperation and provide an alternative to the use of financial side payments to induce countries to cooperate. Two types of interconnected games are distinguished in this paper, i.e. direct sum games and tensor games. In the former all the constituting isolated games are games in strategic form and in the latter they are repeated games. In both cases the interconnected game can be interpreted as a multiple objective game, but only the setting where a trade-off is made for the vector-payoffs is considered. In addition to the formal definition of these types of interconnected games, some elementary results concerning Nash equilibria of such games are derived.Folmer and v. Mouche: Landbouwuniversiteit Wageningen, Postbus 8130, 6700 EW Wageningen, The Netherlands; Ragland: University of Colorado at Boulder, Boulder, Colorado 80309-0256, U.S.A. An earlier version of this paper was presented at the EAERE conference in Stockholm, June 1991. The authors appreciate comments made by conference participants and journal referees.     

Continuous-time games of timing

We address the question of existence of equilibrium in general timing games with complete information. Under weak assumptions, any two-player timing game has a Markov subgame perfect -equilibrium, for each >0. This result is tight. For some classes of games (symmetric games, games with cumulative payoffs), stronger existence results are established.     

Is limit pricing evolutionarily stable?

We have analyzed the question whether or not limit-pricing behavior can be viewed as a strategy, which survives the replicator dynamics in a game in which firms change strategies through imitation. Our results show that, regardless of the proportion of low cost incumbents in the population, potential entrants that play the strategy "enter" when they observe limit output are wiped out. The unique ESS consists of all low cost incumbents playing the "limit output" strategy, and all high cost incumbents playing the "monopoly output". This ESS includes potential entrants playing "stay out" after observing the limit output, and playing "enter" if monopoly output is observed in the first stage. Hence, limit pricing survives the replicator dynamics and appears in the stable state of the population.JEL Classification: B25, C73, L11We would like to thank an anonymous referee for valuable comments on an earlier version of this paper. Correspondence to: U. Soytas     

Dynamics in near-potential games

We consider discrete-time learning dynamics in finite strategic form games, and show that games that are close to a potential game inherit many of the dynamical properties of potential games. We first study the evolution of the sequence of pure strategy profiles under better/best response dynamics. We show that this sequence converges to a (pure) approximate equilibrium set whose size is a function of the “distance” to a given nearby potential game. We then focus on logit response dynamics, and provide a characterization of the limiting outcome in terms of the distance of the game to a given potential game and the corresponding potential function. Finally, we turn attention to fictitious play, and establish that in near-potential games the sequence of empirical frequencies of player actions converges to a neighborhood of (mixed) equilibria, where the size of the neighborhood increases according to the distance to the set of potential games.