A dominance solvable global game with strategic substitutes

Global games emerged as an approach to equilibrium selection. For a general setting with supermodular payoffs, unique selection of equilibrium has been obtained through iterative elimination of strictly dominated strategies. For the case of global games with strategic substitutes, uniqueness of equilibrium has not been proved by iterative elimination of strictly dominated strategies, making the equilibrium less appealing. In this work we provide a condition for dominance solvability in a simple three-player binary-action global game with strategic substitutes. This opens an unexplored research agenda on the study of global games with strategic substitutes.     

Bounds for best response functions in binary games

This paper studies the identification of best response functions in binary games without making strong parametric assumptions about the payoffs. The best response function gives the utility maximizing response to a decision of the other players. This is analogous to the response function in the treatment-response literature, taking the decision of the other players as the treatment, except that the best response function has additional structure implied by the associated utility maximization problem. Further, the relationship between the data and the best response function is not the same as the relationship between the data and the response function in the treatment-response literature. We focus especially on the case of a complete information entry game with two firms. We also discuss the case of an entry game with many firms, non-entry games, and incomplete information. Our analysis of the entry game is based on the observation of realized entry decisions, which we then link to the best response functions under various assumptions including those concerning the level of rationality of the firms, including the assumption of Nash equilibrium play, the symmetry of the payoffs between firms, and whether mixed strategies are admitted.     

Markov Perfect equilibria in repeated asynchronous choice games

This paper examines the issue of multiplicity of Markov Perfect equilibria in alternating move repeated games. Such games are canonical models of environments with repeated, asynchronous choices due to inertia or replacement. Our main result is that the number of Markov Perfect equilibria is generically finite with respect to stage game payoffs. This holds despite the fact that the stochastic game representation of the alternating move repeated game is “non-generic” in the larger space of state dependent payoffs. We further obtain that the set of completely mixed Markov Perfect equilibria is generically empty with respect to stage game payoffs.     

Structure of teams—A cooperative game theory approach

One key task for HR departments and managers is to design the structure of teams in the firm. Two main dimensions when carrying out this decision are the size of the teams and the combination of specialized expertise within the team. In this article, we apply cooperative game theory to model this decision. First, we introduce production games. These games are an enhancement of team games and allow the modeling of teams. Together with the coalition structure approach of cooperative game theory, we analyze two standard situations of team theory.     

What restrictions do Bayesian games impose on the value of information?

In a Bayesian game players play an unknown game. Before the game starts some players may receive a signal regarding the specific game actually played. Typically, information structures that determine different signals, induce different equilibrium payoffs. In two-person zero-sum games the equilibrium payoff measures the value of the particular information structure which induces it. We pose a question as to what restrictions Bayesian games impose on the value of information. We provide answers for two kinds of information structures: symmetric, where both players are equally informed, and one-sided, where only one player is informed.     

On the computation of stable sets for bimatrix games

In this paper, an alternative definition of stable sets, defined by Mertens [Mertens, 1989. Stable equilibria – a reformulation. Part I. Definitions and basic properties. Mathematics of Operations Research 14, 575–625], is given where perturbations are interpreted as restrictions on the strategy space instead of perturbations of the payoffs. This alternative interpretation is then used to compute a special type of stable sets –called standard stable sets – in the context of bimatrix games, exclusively using linear optimization techniques and finite enumerations.     

Coalition formation in general NTU games

A general nontransferable utility (NTU) game is interpreted as a collection of pure bargaining games that can be played by individual coalitions. The threatpoints or claims points respectively, in these pure bargaining games reflect the players' opportunities outside a given coalition. We develop a solution concept for general NTU games that is consistent in the sense that the players' outside opportunities are determined by the solution to a suitably defined reduced game. For any general NTU game the solution predicts which coalitions are formed and how the payoffs are distributed among the players.     

Are CEOs expected utility maximizers?

Are individuals expected utility maximizers? This question represents much more than academic curiosity. In a normative sense, at stake are the fundamental underpinnings of the bulk of the last half-century’s models of choice under uncertainty. From a positive perspective, the ubiquitous use of benefit-cost analysis across government agencies renders the expected utility maximization paradigm literally the only game in town. In this study, we advance the literature by exploring CEO’s preferences over small probability, high loss lotteries. Using undergraduate students as our experimental control group, we find that both our CEO and student subject pools exhibit frequent and large departures from expected utility theory. In addition, as the extreme payoffs become more likely CEOs exhibit greater aversion to risk. Our results suggest that use of the expected utility paradigm in decision making substantially underestimates society’s willingness to pay to reduce risk in small probability, high loss events.     

Learning games

This paper presents a model of learning about a game. Players initially have little knowledge about the game. Through playing the same game repeatedly, each player not only learns which action to choose but also constructs a personal view of the game. The model is studied using a hybrid payoff matrix of the prisoner's dilemma and coordination games. Results of computer simulations show that (1) when all the players are slow at learning the game, they have only a partial understanding of the game, but might enjoy higher payoffs than in cases with full or no understanding of the game; (2) when one player is quick in learning the game, that player obtains a higher payoff than the others. However, all can receive lower payoffs than in the case in which all players are slow learners.     

Cores of many-player games; nonemptiness and equal treatment

This paper provides sufficient conditions to ensure nonemptiness of approximate cores of many-player games and symmetry of approximate core payoffs (the equal treatment property). The conditions are: (a) essential superadditivity—an option open to a group of players is to partition into smaller groups and realize the worths of these groups and (b) small group effectiveness (SGE)—almost all gains to collective activities can be realized by cooperation only within members of some partition of players into relatively small groups. Another condition, small group negligibility (SGN), is introduced and shown to be equivalent to SGE. SGN dictates that small groups of players cannot have significant effects on average (i.e., per capita) payoffs of large populations; thus, SGN is a analogue, for games with a finite player set, of the condition built into models with a continuum of player that sets of measure zero can be ignored. SGE implies per capita boundedness (PCB), that the supremum of average or per capita payoffs is uniformly bounded above. Further characterization of SGE in terms of its relationship to PCB is provided. It is known that if SGE does not hold, then approximate cores of many-player games may be empty. Examples are developed to show that if SGE does not hold and if there are players of “scarce types” (in other works, players with scarce attributes) then even if there is only a finite number of types of players and approximate cores are non-empty, symmetry may be lost; moreover, even players of abundant types may be treated asymmetrically by the core.     

Are “Anti-Folk Theorems” in repeated games nongeneric?

Folk Theorems in repeated games hold fixed the game payoffs, while the discount factor is varied freely. We show that these results may be sensitive to the order of limits in situations where players move asynchronously. Specifically, we show that when moves are asynchronous, then for a fixed discount factor close to one there is an open neighborhood of games which contains a pure coordination game such that every Perfect equilibrium of every game in the neighborhood approximates to an arbitrary degree the unique Pareto dominant payoff of the pure coordination game.     

On axiomatizations of the Shapley value for assignment games

We consider the problem of axiomatizing the Shapley value on the class of assignment games. It turns out that several axiomatizations of the Shapley value on the class of all TU-games do not characterize this solution on the class of assignment games. However, when considering an assignment game as a (communication) graph game where the game is simply the assignment game and the graph is a corresponding bipartite graph where buyers (sellers) are connected with sellers (buyers) only, we show that Myerson’s component efficiency and fairness axioms do characterize the Shapley value on the class of assignment games. Moreover, these two axioms have a natural interpretation for assignment games. Component efficiency yields submarket efficiency stating that the sum of the payoffs of all players in a submarket equals the worth of that submarket, where a submarket is a set of buyers and sellers such that all buyers in this set have zero valuation for the goods offered by the sellers outside the set, and all buyers outside the set have zero valuations for the goods offered by sellers inside the set. Fairness of the graph game solution boils down to valuation fairness stating that only changing the valuation of one particular buyer for the good offered by a particular seller changes the payoffs of this buyer and seller by the same amount.     

Instability in the labor market for researchers

R&D is both an activity which involves team effort, and with many of the features of a zero-sum game. This paper shows that these characteristics make the labor market for researchers unstable in the sense that firms have incentives to continuously change the composition of their research teams. Related results concerning the core of several cooperative games in characteristic form are also proved.     

RECENT ADVANCES IN OLIGOPOLY THEORY FROM A GAME THEORY PERSPECTIVE

Abstract. This paper surveys the contribution that recent developments in game theory have made to the understanding of oligopoly theory. It is argued that conventional models suffer from the problem that there are a number of solution concepts offered with little guidance as to which should be selected, and this is related to the static nature of the models employed. One important development in game theory has been the analysis of repeated games, and when applied to oligopoly theory this suggests that outcomes may be more cooperative than conventional theory suggests. Related to this is the requirement that firms employ credible threats to punish cheating from cooperative outcomes, and the paper examines the extent to which imperfect information may restrict the scope of firms to employ such punishments. One way in which firms may seek to make threats credible is through strategic investments, for example in production capacity, and the paper explores how competition over price or output is integrated with competition over instruments for strategic investment.     

In Support of Trigger Strategies: Experimental Evidence from Two-Person Noncooperative Games

Cooperative equilibria can be supported in a repeated game when players use trigger strategies. This paper tests how well trigger strategies explain behavior in two-person experimental games. Reducing payoffs for choices larger than the Cournot level induces smaller average outputs, behavior generally consistent with trigger strategy models. Reducing payoffs for choices well above the Cournot level will not affect behavior if actions are consistent with a trigger strategy involving longer-lived, less intense punishment phases (the grim-reaper strategy), but would matter for trigger strategies with short-lived but intense punishment phases. Results show that behavior is most consistent with the former.     

COALITION FORMATION AND BARGAINING PROTOCOLS: A REVIEW OF THE LITERATURE

This paper offers a review of the vast literature regarding bargaining and coalition formation. This topic has been generally described as the attempt to provide strategic foundations to cooperative solution concepts. It can therefore be seen as the linking ring between the non‐cooperative and the cooperative game‐theoretic approach to coalition formation. Its central role in economic theory and its relatively long history that goes back to the Nash program have fostered a large academic production, including surveys. Nonetheless, this paper will focus on an aspect that is often neglected in the dedicated surveys: the specificities of the bargaining protocols leading to different outcomes. Although generally downgraded to the rank of details, the differences in bargaining protocols, even when minor, can cause significant changes in fundamental aspects such as the possibility to reach full cooperation, the distribution of final pay‐offs and the time taken to reach an agreement. Focused on externalities‐free games, therefore on bargaining protocols sustaining solution concepts for cooperative games in characteristic function form, the paper aims at providing a brief but exhaustive review of the topic that could result in a very useful tool for any researcher approaching the subject of coalitional bargaining.     

A note on the multiple partners assignment game

In the assignment game of Shapley and Shubik [Shapley, L.S., Shubik, M., 1972. The assignment game. I. The core, International Journal of Game Theory 1, 11–130] agents are allowed to form one partnership at most. That paper proves that, in the context of firms and workers, given two stable payoffs for the firms there is a stable payoff which gives each firm the larger of the two amounts and also one which gives each of them the smaller amount. Analogous result applies to the workers. Sotomayor [Sotomayor, M., 1992. The multiple partners game. In: Majumdar, M. (Ed.), Dynamics and Equilibrium: Essays in Honor to D. Gale. Mcmillian, pp. 322–336] extends this analysis to the case where both types of agents may form more than one partnership and an agent's payoff is multi-dimensional. Instead, this note concentrates in the total payoff of the agents. It is then proved the rather unexpected result that again the maximum of any pair of stable payoffs for the firms is stable but the minimum need not be, even if we restrict the multiplicity of partnerships to one of the sides.     

基于区间二型模糊集的VIKOR多属性决策方法研究

针对传统VIKOR方法不能处理不确定语言信息的缺陷,本文在VIKOR方法的基础上提出了一种基于区间二型模糊的VIKOR扩展方法用于解决多属性决策问题。首先介绍了区间二型模糊的概念、运算法则,接着定义了一种新的计算区间二型模糊集之间的距离公式,在此基础上提出基于区间二型模糊的VIKOR扩展方法。最后,通过一个算例说明该方法的有效性和合理性。