|
on Game Theory |
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Issue of 2012‒01‒25
twenty papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Rene van den Brink (VU University Amsterdam); Chris Dietz (VU University Amsterdam) |
| Abstract: | A situation in which a finite set of agents can generate certain payoffs by cooperation can be described by a cooperative game with transferable utility (or simply a TU-game) where each agent is represented by one player in the game. In this paper, we assume that one agent can be represented by more than one player. We introduce two solutions for this multi-player agent game model, both being generalizations of the Shapley value for TU-games. The first is the agent-Shapley value and considers the agents in the most unified way in the sense that when an agent enters a coalition then it enters with all its players. The second is the player-Shapley value which takes all players as units, and the payoff of an agent is the sum of the payoffs over all its players. We provide axiomatic characterizations of these two solutions that differ only in a collusion neutrality axiom. The agent-Shapley value satisfies player collusion neutrality stating that collusion of two players belonging to the same agent does not change the payoff of this agent. On the other hand, the player-Shapley value satisfies agent collusion neutrality stating that after a collusion of two agents, the sum of their payoffs does not change. After axiomatizing the player- and agent-Shapley values we apply them to airport games and voting games. |
| Keywords: | Cooperative TU-game; Shapley value; multi-player agent; collusion neutrality; airport games |
| JEL: | C71 |
| Date: | 2012–01–02 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20120001&r=gth |
| By: | Sergio Currarini (Department of Economics,Faculty of Economics, Università degli Studi di Venezia "Ca' Foscari"); Marco Marini (Department of Economics, Society & Politics, Università di Urbino "Carlo Bo" and CREI, Università di Roma III) |
| Abstract: | In this paper we review a number of coalitional solution concepts for the analysis of the stability of cartels and mergers under oligopoly. We show that, although so far the industrial organization and the cooperative game-theoretic literature have proceeded somehow independently on this topic, the two approaches are highly inter-connected. We first consider the basic problem of the stability of the whole industry association of firms under oligopoly and, for this purpose, we introduce the concept of core in games with externalities. We show that different assumptions on the behaviour as well as on the timing of the coalitions of firms yield very di¤erent results on the set of allocations which are core-stable. We then consider the stability of associations of firms organized in coalition structures different from the grand coalition. To this end, various coalition formation games recently introduced by the so called endogenous coalition formation literature are critically reviewed. Again, di¤erent assumptions concerning the timing and the behaviout of firms are shown to yield a wide range of different results. |
| Keywords: | Cooperative Games, Coalitions, Mergers, Cartels, Core, Games with Externalities, Endogenous Coalition Formation. |
| JEL: | C70 C71 D23 D43 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:urb:wpaper:11_13&r=gth |
| By: | Francoise Forges; Roberto Serrano |
| Abstract: | This is a brief survey describing some of the recent progress and open problems in the area of cooperative games with incomplete information. We discuss exchange economies, cooperative Bayesian games with orthogonal coalitions, and issues of cooperation in non-cooperative Bayesian games. |
| Keywords: | # |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:bro:econwp:2011-15&r=gth |
| By: | Archie C. Chapman (The University of Sydney Business School); David S. Leslie (The University of Bristol); Alex Rogers (The University of Southampton); Nicholas R. Jennings (The University of Southampton) |
| Abstract: | In this paper, we address the problem of convergence to Nash equilibria in games with rewards that are initially unknown and which must be estimated over time from noisy observations. These games arise in many real-world applications, whenever rewards for actions cannot be prespecified and must be learned on-line. Standard results in game theory, however, do not consider such settings. Specifically, using results from stochastic approximation and differential inclusions, we prove the convergence of variants of fictitious play and adaptive play to Nash equilibria in potential games and weakly acyclic games, respectively. These variants all use a multi-agent version of Q-learning to estimate the reward functions and a novel form of the e-greedy decision rule to select an action. Furthermore, we derive e-greedy decision rules that exploit the sparse interaction structure encoded in two compact graphical representations of games, known as graphical and hypergraphical normal form, to improve the convergence rate of the learning algorithms. The structure captured in these representations naturally occurs in many distributed optimisation and control applications. Finally, we demonstrate the efficacy of the algorithms in a simulated ad hoc wireless sensor network management problem. |
| Keywords: | Game theory, distributed optimisation, learning in games. |
| Date: | 2011–08 |
| URL: | http://d.repec.org/n?u=RePEc:syb:wpbsba:05/2011&r=gth |
| By: | Konrad, Kai A.; Kovenock, Dan |
| Abstract: | 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 subgame perfect equilibria in which all players employ pure strategies or all players play identical mixed strategies in the first stage. We find that the partitioning of prizes allows for coordination failure among players when they play nondegenerate mixed strategies and this can shelter rents and reduce rent dissipation compared to some of the less efficient pure strategy equilibria. -- |
| Keywords: | All-pay contest,multiple prizes,rent dissipation,lifeboat |
| JEL: | D72 D74 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbfff:spii2011106&r=gth |
| By: | Duffy, Sean; Smith, John |
| Abstract: | We find that differences in the ability to devote cognitive resources to a strategic interaction imply differences in strategic behavior. In our experiment, we manipulate the availability of cognitive resources by applying a differential cognitive load. In cognitive load experiments, subjects are directed to perform a task which occupies cognitive resources, in addition to making a choice in another domain. The greater the cognitive resources required for the task implies that fewer such resources will be available for deliberation on the choice. Although much is known about how subjects make decisions under a cognitive load, little is known about how this affects behavior in strategic games. We run an experiment in which subjects play a repeated multi-player prisoner's dilemma game under two cognitive load treatments. In one treatment, subjects are placed under a high cognitive load (given a 7 digit number to recall) and subjects in the other are placed under a low cognitive load (given a 2 digit number). We find that the behavior of the subjects in the low load condition converges to the Subgame Perfect Nash Equilibrium prediction at a faster rate than those in the high load treatment. However, we do not find the corresponding relationship involving outcomes in the game. Specifically, there is no evidence of a significantly different convergence of game outcomes across treatments. As an explanation of these two results, we find evidence that low load subjects are better able to condition their behavior on the outcomes of previous periods. |
| Keywords: | cognitive resources; experimental economics; experimental game theory; public goods game |
| JEL: | C72 C91 |
| Date: | 2012–01–11 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:35906&r=gth |
| By: | Ahmed Doghmi, National Institute of Statistics and Applied Economics, Madinat Al Irfane, Rabat Institutes, 13000 Rabat, Morocco; Abderrahmane ZIAD, University of Caen Basse-Normandie, CREM (UMR CNRS) |
| Abstract: | An agent is said to be partially honest if he or she weakly prefers an outcome at a strategy profile with his truthful strategy than an outcome at a strategy profile with his false strategy, then this player must prefer strictly the \true" strategy profille to the \false" strategy profile. In this paper we consider an exchange economy with single peaked preferences. With many agents (n ≥3), if there exists at least one partially honest agent, we prove that any solution of the problem of fair division satisfying unanimity is Nash implementable. |
| Keywords: | Nash implementation; Partial honesty; Single-peaked preferences |
| JEL: | C72 D71 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:tut:cremwp:201201&r=gth |
| By: | Wieland Mueller; Fangfang Tan |
| Abstract: | Previous experimental results on one-shot sequential two-player games show that group decisions are closer to the subgame-perfect Nash equilbirum than individual decisions. We extend the analysis of inter-group versus inter-individual decision making to a Stackelberg market game, by running both one-shot and repeated markets. Whereas in the one-shot markets we find no significant differences in the behavior of groups and individuals, we find that the behavior of groups is further away from the subgame-perfect equilibrium of the stage game than that of individuals. To a large extent, this result is independent of the method of eliciting choices (sequential or strategy method) and the method used to account for observed first- and second-mover behavior. We provide evidence on followers' response functions and electronic chats to offer an explanation for the differential effect that the time horizon of interaction has on the extent of individual and group players (non)conformity with subgame perfectness. |
| Keywords: | Stackelberg market, groups versus individuals, discontinuity effect, experiment |
| JEL: | C72 C92 L13 |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:who_acts_more_like_a_game_theorist&r=gth |
| By: | Giovanna Devetag; Hykel Hosni; Giacomo Sillari |
| Abstract: | This paper presents the results of an experiment on mutual versus common knowl- edge of advice in a two-player weak-link game with random matching. Our experimen- tal subjects play in pairs for thirteen rounds. After a brief learning phase common to all treatments, we vary the knowledge levels associated with external advice given in the form of a suggestion to pick the strategy supporting the payoff-dominant equilib- rium. In the mutual knowledge of level 1 treatment, the suggestion appears on every subject's monitor at the beginning of every round, with no common knowledge that everybody sees the same suggestion. In the mutual knowledge of level 2 treatment, the same suggestion appears on each subject's monitor, accompanied by the request to "send" the suggestion to the partner in the round, followed by a notification that the message has been read. Finally, in the common knowledge treatment, the suggestion is read aloud by the experimenter at the end of the learning phase. Our results are somewhat surprising and can be summarized as follows: in all our treatments both the choice of the efficiency-inducing action and the percentage of efficient equilibrium play are higher with respect to the control treatment, revealing that even a condition as weak as mutual knowledge of level 1 is sufficient to significantly increase the salience of the efficient equilibrium with respect to the absence of advice. Furthermore, and contrary to our hypothesis, mutual knowledge of level 2 (as the one occurring in our "message" treatment) induces successful coordination more frequently than common knowledge. |
| Keywords: | Coordination games; experimental philosophy; epistemic attitudes, weak-link game; conventions |
| JEL: | D01 D83 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:trn:utwpce:1201&r=gth |
| By: | Mikhail Golosov (Yale University and NES); Vasiliki Skreta (New York University, Stern School of Business); Aleh Tsyvinski (Yale University and NES); Andrea Wilson (New York University) |
| Abstract: | This paper studies strategic information transmission in a dynamic environment where, each period, a privately informed expert sends a message and a decision maker takes an action. Our main result is that, in contrast to a static environment, full information revelation is possible. The gradual revelation of information and the eventual full revelation is supported by the dynamic rewards and punishments. The construction of a fully revealing equilibrium relies on two key features. The first feature is that the expert is incentivized, via appropriate actions, to join separable groups in which she initially pools with far-away types, then later reveals her type. The second feature is the use of trigger strategies. The decision maker is incentivized by the reward of further information revelation if he chooses the separation-inducing actions, and the threat of a stop in information release if he does not. Our equilibrium is non-monotonic. With monotonic partition equilibria, full revelation is impossible. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:eie:wpaper:1110&r=gth |
| By: | Hübner, Frank |
| Abstract: | Die von Gale und Shapley in ihrem 1962 veröffentlichten Artikel College Admissions and the Stability of Marriage vorgestellte deferred acceptance procedure hat in der Literatur zu einer umfassenden Diskussion über Zuordnungsverfahren auf zweiseitigen Märkten geführt, die sich mit der Fragestellung beschäftigen, wie die Agenten zweier disjunkter Mengen anhand gegenseitiger Präferenzlisten einander zugeordnet werden können. Dem von Gale und Shapley vorgestellten Algorithmus kam dabei in den letzten Jahren nicht nur in der Theorie eine große Bedeutung zu, sondern auch in der Praxis wird dem Versagen zahlreicher Märkte mit solchen Mechanismen entgegengetreten. Diese Arbeit geht ausführlich auf die von Gale und Shapley entwickelte deferred acceptance procedure und die sich hieraus ergebenden Manipulationsanreize auf zweiseitigen Märkten anhand des Hochzeits- und college admissions-Problems ein. Die im jeweiligen Modell resultierenden Manipulationsanreize werden in vier Arten von Manipulationen gegliedert - die Manipulation anhand von Präferenzen, anhand vorzeitiger bilateraler Vereinbarungen, anhand von endowments und anhand der Quote - und jeweils miteinander verglichen. Dabei wird deutlich, dass weder die deferred acceptance procedure noch irgendein anderes Zuordnungsverfahren, das stabile Zuordnungen ergibt, vollständig immun gegen Manipulationen ist. Anhand zahlreicher Theoreme und Überlegungen kann jedoch gezeigt werden, dass die Anreize oft nur für eine Seite des Marktes existieren und bei größer werdenden Märkten in der Praxis sogar abnehmen. -- The deferred acceptance procedure introduced by Gale and Shapley in their article College Admissions and the Stability of Marriage (1962) led to a huge and still growing discussion in the literature on two-sided matching markets. The algorithm didn't only become important in theory but is also often used in practice by policymakers to confront market failure. This paper explains the deferred acceptance procedure in detail and presents a survey on the resulting manipulability on twosided matching markets, e.g., within the marriage and college admissions problem. The incentives to manipulate are categorized in four groups of manipulations - manipulation via preferences, via pre-arranged matches, via endowments and via capacities - and are then compared for both problems. It is shown that there exists no stable matching procedure that is strategy-proof for all agents. But in practice many incentives to manipulate only apply to one side of the market and decrease with the size of the market. |
| Keywords: | Matching,university admission,manipulation,strategic behavior |
| JEL: | C78 D78 I29 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbmbh:spii2011203&r=gth |
| By: | Achille Basile (Università di Napoli Federico II and CSEF); Maria Gabriella Graziano (Università di Napoli Federico II and CSEF); Maria Laura Pesce (Università di Napoli Federico II) |
| Abstract: | The paper proposes a notion of fairness which overcomes the conflict arising between efficiency and the absence of envy in economies with uncertainty and asymmetrically informed agents. We do it in general economies which include, as particular cases, the main differential information economies studied in the literature. The analysis is further extended by allowing the presence of large traders, which may cause the lack of perfect competition. |
| Keywords: | Mixed markets, fairness, envy, efficiency, asymmetric information |
| JEL: | C71 D51 D82 |
| Date: | 2012–01–11 |
| URL: | http://d.repec.org/n?u=RePEc:sef:csefwp:303&r=gth |
| By: | Tiago P. Peixoto; Stefan Bornholdt |
| Abstract: | We investigate the dynamics of a trust game on a mixed population where individuals are forced to play against a predetermined number of partners, who they choose dynamically. Agents are also allowed to adapt their level of trustworthiness, based on payoff. The dynamics undergoes a transition at a specific value of the strategy update rate, above which an emergent cartel organization is observed, where individuals have similar values of below optimal trustworthiness. This cartel organization is not due to an explicit collusion among agents; instead it arises spontaneously from the maximization of the individual payoffs. This dynamics is marked by large fluctuations and a high degree of unpredictability for most of the parameter space, and serves as a plausible qualitative explanation for observed elevated levels and fluctuations of certain commodity prices. |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1201.3798&r=gth |
| By: | Kai A. Konrad; Florian Morath |
| Abstract: | We study conflict between two groups of individuals. Using Schaffer's (1988) concept of evolutionary stability we provide an evolutionary underpinning for in-group altruism combined with spiteful behavior towards members of the rival out-group. We characterize the set of evolutionarily stable combinations of in-group favoritism and out-group spite and find that an increase in in-group altruism can be balanced by a decrease in spiteful behavior towards the out-group. |
| Keywords: | altruism, spite, in-group favoritism, conflict, evolutionary stability, indirect evolutionary approach |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:mpi:wpaper:evolutionarily_stable&r=gth |
| By: | Reddy, P.V.; Schumacher, J.M.; Engwerda, J.C. (Tilburg University, Center for Economic Research) |
| Abstract: | Abstract: In this article we analyze how the presence of thresholds influences multi agent decision making situations. We introduce a class of discounted autonomous optimal control problems with threshold effects and discuss tools to analyze these problems. Later, using these results we investigate two types of threshold effects; namely, simple and hysteresis switching, in the canonical model of the shallow lake. We solve the optimal management and open loop Nash equilibrium solutions for the shallow lake model with threshold effects. We establish a bifurcation analysis of the optimal vector field. Further, we observe that modeling with threshold effects simplifies this analysis. To be precise, the bifurcation scenarios rely on simple rules (inequalities) which can be verified easily. However, the qualitative behavior of the switching vector field is similar to the smooth case. |
| Keywords: | Optimal control;Differential games;Threshold effects;Discontinuous dynamics;Shallow lake. |
| JEL: | C61 Q57 |
| Date: | 2012 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:kubcen:2012001&r=gth |
| By: | Litsa Alexandra, University of Caen Basse-Normandie, Center of Research in Economics and Management, Caen, France; Maguet Jean-François, University of Caen Basse-Normandie, Center of Research in Economics and Management, Caen, France |
| Abstract: | Taking as a starting point the theory of matching applied in the case of a problem of college admissions, where one is interested only to strict preference profiles for students and colleges, a part of the literature has been oriented towards profiles of priorities for colleges. In this paper we will assume that students have also their own priorities to which is associated some 'fuzzy'. This vagueness designates the preference of an individual (resp. college) for a college relative to parameters that characterize the latter one (resp. individual). Thus, we talk about fuzzy priorities. Our purpose is to analyze this aspect and to propose a real-life mechanism which will take into consideration the fuzzy priority profiles of both students and colleges, in order to achieve the best possible matching that is stable, strategy-proof, Pareto efficient and fair. |
| Keywords: | Education, Priorities, Preferences, Fuzzy, Algorithm, Matching |
| JEL: | C78 D80 I20 I31 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:tut:cremwp:201202&r=gth |
| By: | Sarah Jacobson (Williams College); Jason Delaney (University of Arkansas at Little Rock) |
| Abstract: | Some policy problems pit the interests of one group against those of another group. One group may, for example, determine the provision of a project (such as a power plant or a dam) that benefits group members but has downstream externalities that hurt people outside the group. We introduce a model of projects with such asymmetries. In-group members may contribute to a common fund that benefits them as a public good. In the model, benefits from the project may or may not vary within the group. Project provision has negative downstream externalities: common fund contributions hurt agents outside the in-group (“Outsiders”) rendering common fund contributions anti-social overall. Many models of social preferences predict that such externalities should reduce or eliminate project provision, although conditional cooperation or a preference for in-group members may counteract this effect. We test this model with a lab experiment. With homogeneous in-group benefits, the presence of negative downstream externalities reduces contribution levels by nearly half. We introduce a rotating high-return position that allows subjects to trade favors. Contributions diminish only slightly with the introduction of the negative externality and reciprocal giving occurs whether or not Outsiders are present. |
| Keywords: | public bad, public good, social preferences, reciprocity, externalities, in-group-out-group, parochial altruism |
| JEL: | C91 D01 D62 D71 H41 Q50 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:wil:wileco:2012-03&r=gth |
| By: | Thorsten Chmura (Department of Economics, Ludwig-Maximilians-Universitat Munich); Sebastian Goerg (Max Planck Institute for Research on Collective Goods, Bonn); Reinhard Selten (cLaboratory for Experimental Economics (BonnEconLab), University of Bonn) |
| Abstract: | In this paper, we introduce two new learning models: impulse-matching learning and action-sampling learning. These two models together with the models of self-tuning EWA and reinforcement learning are applied to 12 different 2 x 2 games and their results are compared with the results from experimental data. We test whether the models are capable of replicating the aggregate distribution of behavior, as well as correctly predicting individuals' round-by-round behavior. Our results are two-fold: while the simulations with impulse-matching and action-sampling learning successfully replicate the experimental data on the aggregate level, individual behavior is best described by self-tuning EWA. Nevertheless, impulse-matching learning has the second highest score for the individual data. In addition, only self-tuning EWA and impulse-matching learning lead to better round-by-round predictions than the aggregate frequencies, which means they adjust their predictions correctly over time. |
| Keywords: | learning, 2 x 2 games, Experimental data |
| JEL: | C92 C72 C91 |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2011_26&r=gth |
| By: | Takahiro Watanabe (Department of Business Administration, Tokyo Metropolitan University) |
| Abstract: | A game in which an incumbent and an entrant decide the timings of entries into a new market is investigated. The profit flows involve two uncertain factors: (1) the basic level of the demand of the market observed only by the incumbent and (2) the fluctuation of the profit flow described by a geometric Brownian motion that is common to both firms. The optimal timing for the incumbent, who privately knows the high demand, is earlier than that for the low-demand incumbent. This earlier entrance, however, reveals the information of the high demand to the entrant, so that the entrant observing the timing of the incumbent would accelerate the its own timing of the investment that reduces the monopolistic profit of the incumbent. Therefore, the high-demand incumbent may delay the timing of the investment in order to hide the information strategically. The equilibria of this signaling game are characterized, and the conditions for the manipulative revelation are investigated. The values of both firms are compared with the case of complete information. |
| Keywords: | Real Option, Investment Timing, Signaling, Asymmetric Information, Game Theory |
| JEL: | G31 D81 C73 |
| Date: | 2012–01 |
| URL: | http://d.repec.org/n?u=RePEc:kyo:wpaper:809&r=gth |
| By: | Konrad, Kai A. |
| Abstract: | This paper surveys some of the strategic aspects that emerge if players fight in an alliance against an enemy. The survey includes the free-rider problem and the hold-up problem that emerges in the baseline model, the role of supermodularity in alliance members' effort contributions, the role of budget constraints, the role of information transfer inside the alliance, and the role of in-group favoritism. -- |
| Keywords: | Alliances,contests,conflict,in-group favoritism |
| JEL: | D72 D74 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:wzbfff:spii2011105&r=gth |