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on Game Theory |
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Issue of 2011‒11‒14
twenty papers chosen by Laszlo A. Koczy Hungarian Academy of Sciences and Obuda University |
| By: | Antonio Romero-Medina; Matteo Triossi |
| Abstract: | Studying the interaction between preference and capacity manipulation in matching markets, we prove that acyclicity is a necessary and su!cient condition that guarantees the stability of a Nash equilibrium and the strategy-proofness of truthful capacity revelation under the hospital-optimal and intern-optimal stable rules. we then introduce generalized capacity manipulations games where hospitals move first and state their capacities, and interns are subsequently assigned to hospitals using a sequential mechanism. In this setting, we first consider stable revelation mechanisms and introduce conditions guaranteeing the stability of the outcome. Next, we prove that every stable non-revelation mechanism leads to unstable allocations, unless restrictions on the preferences of the agents are introduced. JEL Classification Numbers: C71, C78, D71, D78. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:edj:ceauch:280&r=gth |
| By: | Ulrike Vollstädt (International Max Planck Research School on Adapting Behavior in a Fundamentally Uncertain World, University of Jena) |
| Abstract: | Bargaining is prevalent in economic interactions. Under complete information, game theory predicts efficient bargaining outcomes (immediate acceptance of first offer) (see Rubinstein, 1982). However, continuous rejections of offers leading to inefficient delays (escalation) have regularly been found in previous bargaining experiments even under complete information (see Roth, 1995). I test experimentally (1) whether power asymmetry leads to more escalation in bargaining and (2) whether perspective-taking reduces escalation. I find that power asymmetry increases escalation, but that perspective-taking does not reduce escalation. |
| Keywords: | two-person bargaining experiment, asymmetric power, escalation, perspective-taking |
| JEL: | C78 D89 |
| Date: | 2011–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2011-054&r=gth |
| By: | Chatterjee, Kalyan (Department of Economics, The Pennsylvania State University); Dutta, Bhaskar (Department of Economics,University of Warwick) |
| Abstract: | This paper studies a model of diffusion in a fixed, finite connected network. There is an interested party that knows the quality of the product or idea being propagated and chooses an implant in the network to influence other agents to buy or adopt. Agents are either “innovators”, who adopt immediately, or rational. Rational consumers buy if buying rather than waiting maximizes expected utility. We consider the conditions on the network under which efficient diffusion of the good product with probability one is a perfect Bayes equilibrium. Centrality measures and the structure of the entire network are both important. We also discuss various inefficient equilibria. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:wrk:warwec:972&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics); Alexandre Skoda (Centre d'Economie de la Sorbonne) |
| Abstract: | We study cooperative games associated with a communication structure which takes into account a level of communication between players. Let us consider an undirected communication graph : each node represents a player and there is an edge between two nodes if the corresponding players can communicate directly. Moreover we suppose that a weight is associated with each edge. We compute the so-called strength of this graph and use the corresponding partition to determine a particular coalition structure. The strength of a graph is a measure introduced in graph theory to evaluate the resistance of networks under attacks. It corresponds to the minimum on all subsets of edges of the ratio between the sum of the weights of the edges and the number of connected components created when the set of edges is suppressed from the graph. The set of edges corresponding to the minimum ratio induces a partition of the graph. We can iterate the calculation of the strength on the subgraphs of the partition to obtain refined partitions which we use to define a hierarchy of coalition structures. For a given game on the graph, we build new games induced by these coalition structures and study the inheritance of convexity properties, and the Shapley value associated with them. |
| Keywords: | Communication networks, coalition structures, cooperative games. |
| JEL: | C71 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:11059&r=gth |
| By: | Matthias Kräkel |
| Abstract: | Participants of dynamic competition games may prefer to play with the rules of the game by systematically withholding e¤ort in the beginning. Such behavior is referred to as sandbagging. I consider a two-period con- test between heterogeneous players and analyze potential sandbagging of high-ability participants in the first period. Such sandbagging can be ben- eficial to avoid second-period matches against other high-ability opponents. I characterize the conditions under which sandbagging leads to a coordina- tion problem, similar to that of the battle-of-the sexes game. Moreover, if players' abilities have a stronger impact on the outcome of the first-period contest than e¤ort choices, mutual sandbagging by all high-ability players can arise. |
| Keywords: | ecoordination problem, dynamic contest, heterogeneous contestants, withholding e¤ort |
| JEL: | C72 D72 |
| Date: | 2011–11 |
| URL: | http://d.repec.org/n?u=RePEc:bon:bonedp:bgse11_2012&r=gth |
| By: | Laszlo A. Koczy (Institute of Economics - Hungarian Academy of Sciences); Mikl¢s Pinter (Department of Mathematics - Corvinus University Budapest) |
| Abstract: | Voting power in voting situations is measured by the probability of changing decisions by altering the cast 'yes' or 'no' votes. Recently this analysis has been extended by strategic abstention. Abstention, just as 'yes' or 'no' votes can change decisions. This theory is often applied to weighted voting situations, where voters can cast multiple votes. Measuring the power of a party in a national assembly seems to fit this model, but in fact its power comprises of votes of individual representatives each having a single vote. These representatives may vote yes or no, or may abstain, but in some cases they are not even there to vote. We look at absentees not due to a conscious decision, but due to illness, for instance. Formally voters will be absent, say, ill, with a certain probability and only present otherwise. As in general not all voters will be present, a thin majority may quickly melt away making a coalition that is winning in theory a losing one in practice. A simple model allows us to differentiate between winning and more winning and losing and less losing coalitions reected by a voting game that is not any more simple. We use data from Scotland, Hungary and a number of other countries both to illustrate the relation of theoretical and effective power and show our results working in the practice. |
| Keywords: | a priori voting power; power index; being absent from voting; minority; Shapley-Shubik index; Shapley value |
| JEL: | C71 D72 |
| Date: | 2011–06 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1129&r=gth |
| By: | Antonio Romero-Medina; Matteo Triossi |
| Abstract: | This paper analyzes the role of acyclicity in singleton cores. We show that the absence of simultaneous cycles is a sufficient condition for the existence of singleton cores. Furthermore, acyclicity in the preferences of either side of the market is a minimal condition that guarantees the existence of singleton cores. If firms or workers preferences are acyclical, unique stable matching is obtained through a procedure that resembles a serial dictatorship. Thus, acyclicity generalizes the notion of common preferences. It follows that if the firms or workers preferences are acyclical, unique stable matching is strongly efficient for the other side of the market. JEL Classification Numbers: C71, C78, D71. |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:edj:ceauch:281&r=gth |
| By: | Peter Biro (Institute of Economics - Hungarian Academy of Sciences); Flip Klijn (Institute for Economic Analysis (CSIC), Spain) |
| Abstract: | This survey deals with two-sided matching markets where one set of agents (workers/residents) has to be matched with another set of agents (firms/hospitals). We first give a short overview of a selection of classical results. Then, we review recent contributions to a complex and representative case of matching with complementarities, namely matching markets with couples. We discuss contributions from computer scientists, economists, and game theorists. |
| Keywords: | matching; couples; stability; computational complexity; incentive compatibility; restricted domains; large markets |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1139&r=gth |
| By: | Peter H. Kriss; Andreas Blume; Roberto A. Weber |
| Abstract: | We examine communication in a two-player coordination game with Pareto-ranked equilibria. Prior research demonstrates that efficient coordination is difficult without communication but obtains regularly with (mandatory) costless pre-play messages. In a laboratory experiment, we introduce two realistic features of communication by making the sending of messages optional and costly. Even small costs dramatically reduce message use, but efficient coordination of actions occurs with similar frequency to that observed under costless communication. By varying communication costs we corroborate several predictions from a theoretical analysis based on forward induction. Our results indicate that, for some levels of communication costs, explicit communication may be unnecessary for efficient coordination; instead, players simply need to know that the option to send messages was available. Thus, the relationship between communication and coordination is more complex than suggested by prior research. |
| Keywords: | Coordination, communication, experiment |
| JEL: | C72 C92 D83 |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:034&r=gth |
| By: | Michel Grabisch (Centre d'Economie de la Sorbonne - Paris School of Economics); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne - Paris School of Economics) |
| Abstract: | The paper concerns a dynamic model of influence in which agents have to make a yes-no decision. Each agent has an initial opinion, which he may change during different phases of interaction, due to mutual influence among agents. The influence mechanism is assumed to be stochastic and to follow a Markov chain. In the paper, we investigate a model of influence based on aggregation functions. Each agent modifies his opinion independently of the others, by aggregating the current opinion of all agents, possibly including himself. We provide a general analysis of convergence in the aggregation model and give more practical conditions based on influential players. We show that the process of influence converges always to one of the two consensus states, and there may exist other terminal classes, which are either cyclic or union of Boolean lattices. We give sufficient conditions for avoiding these additional terminal classes, based on properties of the graph of influence and influential players. We also introduce the notion of influential coalition and show that it can fully describe terminal classes. Some important families of aggregation functions are discussed. |
| Keywords: | Influence, aggregation function, convergence, terminal class, infuential coalition, social network. |
| JEL: | C7 D7 |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:11058&r=gth |
| By: | Sven Fischer (Max Planck Institute for Research on Collective Goods, Bonn); Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group) |
| Abstract: | In three party ultimatum games the proposer can first decide whether to exclude one responder, what increases the available pie. The experiments control for intentionality of exclusion and veto power of the third party. We do not find evidence for indirect reciprocity of the remaining responder after the exclusion of the other. Similarly, not excluding the second responder is only insignificantly reciprocated by it. Overall, we find little evidence that intentional exclusion has substantial effects on behavior. |
| Keywords: | Exclusion, bargaining, ultimatum game, social preferences, experiment |
| JEL: | C91 J52 |
| Date: | 2011–11–07 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2011-053&r=gth |
| By: | Paulo Barelli (University of Rochester); Spyros Galanis (University of Southampto) |
| Abstract: | We develop an approach to providing epistemic conditions for admissible behavior in games. Instead of using lexicographic beliefs to capture infinitely less likely conjectures, we postulate that players use tie-breaking sets to help decide among strategies that are outcome-equivalent given their conjectures. A player is event-rational if she best responds to a conjecture and uses a list of subsets of the other players' strategies to break ties among outcome-equivalent strategies. Using type spaces to capture interactive beliefs, we show that common belief of event-rationality (RCBER) implies that players play strategies in S1W, that is, admissible strategies that also survive iterated elimination of dominated strategies (Dekel and Fudenberg (1990)). We strengthen standard belief to validated belief and we show that event-rationality and common validated belief of event-rationality (RCvBER) implies that players play iterated admissible strategies (IA). We show that in complete, continuous and compact type structures, RCBER and RCvBER are nonempty, and hence we obtain epistemic criteria for SinfW and IA. |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:roc:rocher:568&r=gth |
| By: | Matros, Alexander; Smirnov, Vladimir |
| Abstract: | We study an R&D race where the prize value is common knowledge, but the search costs are unknown ex ante. The race is modeled as a multistage game with observed previous actions. We provide a characterization of the efficient symmetric Markov perfect equilibrium in both single-player and multiple-player settings. There are two types of inefficiency in search for multiple players in comparison with a single player: a tragedy of the commons (for short races) and free riding (for long races). We demonstrate that there is no monotonicity for three or more players; players can be better off if the race is longer, even though such a race is more costly, and a longer race may take less time to finish. |
| Keywords: | uncertainty; search; R&D |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:syd:wpaper:2123/7867&r=gth |
| By: | Ioannou, Christos A.; Qi, Shi; ,; Rustichini, Aldo |
| Abstract: | Group membership affects an agent's individual behavior. We determine how, by testing two competing hypotheses. One is that group membership operates through social identity, and the other is that group membership implements a correlation among the actions of in-group members in response to an implicit signal. We introduce two novel features in the experimental design. The first feature is the display of group outcomes. This allows us to assess directly the importance of relative group performance on subjects' decisions. The second is a careful manipulation of the Dictator game and the Trust game. More specifically, we choose parameters strategically so as to ensure no change in the pecuniary incentives across the two games. For a precise quantitative test of the two hypotheses we develop a structural model to describe an agent's behavior across treatments. Our findings suggest that the role of social identity on motivating agents' decisions has been exaggerated. The display of group outcomes induces a group effect, but a careful analysis of this effect reveals that participants use group outcomes as a signal to coordinate in-group members on favorable outcomes. Furthermore, we find evidence in support of recent experimental studies which demonstrate that an agent's allocation choice is sensitive to the behavior of the agent that generated the choice set. |
| Date: | 2011–05–01 |
| URL: | http://d.repec.org/n?u=RePEc:stn:sotoec:1106&r=gth |
| By: | Rudolf Berghammer (Institut für Informatik - Universität Kiel); Agnieszka Rusinowska (Centre d'Economie de la Sorbonne); Harrie de Swart (Faculty of Philosophy - Erasmus University Rotterdam) |
| Abstract: | We describe a simple computing technique for the tournament choice problem. It rests upon a relational modeling and uses the BDD-based computer system RelView for the evaluation of the relation-algebraic expressions that specify the solutions and for the visualization of the computed results. The Copeland set can immediately be identified using RelView's labeling feature. Relation-algebraic specifications of the Condorcet non-losers, the Schwartz set, the top cycle, the uncovered set, the minimal covering set, the Banks set, and the tournament equilibrium set are delivered. We present an example of a tournament on a small set of alternatives, for which the above choice sets are computed and visualized via RelView. The technique described in this paper is very flexible and especially appropriate for prototyping and experimentation, and as such very instructive for educational purposes. It can easily be applied to other problems of social choice and game theory. |
| Keywords: | Tournament, relational algebra, REL VIEW, Copeland set, Condorcet non-losers, Schwartz set, top cycle, uncovered set, minimal covering set, Banks set, tournament equilibrium set. |
| JEL: | D71 C63 C88 |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:mse:cesdoc:11067&r=gth |
| By: | Peter Biro (Institute of Economics - Hungarian Academy of Sciences); Gethin Norman (School of Computing Science - University of Glasgow) |
| Abstract: | Suppose that the agents of a matching market contact each other randomly and form new pairs if is in their interest. Does such a process always converge to a stable matching if one exists? If so, how quickly? Are some stable matchings more likely to be obtained by this process than others? In this paper we are going to provide answers to these and similar questions, posed by economists and computer scientists. In the first part of the paper we give an alternative proof for the theorems by Diamantoudi et al. and Inarra et al. which implies that the corresponding stochastic processes are absorbing Markov chains. Our proof is not only shorter, but also provides upper bounds for the number of steps needed to stabilise the system. The second part of the paper proposes new techniques to analyse the behaviour of matching markets. We introduce the Stable Marriage and Stable Roommates Automaton and show how the probabilistic model checking tool PRISM may be used to predict the outcomes of stochastic interactions between myopic agents. In particular, we demonstrate how one can calculate the probabilities of reaching different matchings in a decentralised market and determine the expected convergence time of the stochastic process concerned. We illustrate the usage of this technique by studying some well-known marriage and roommates instances and randomly generated instances. |
| Keywords: | roommates problem, marriage problem, stochastic processes, core convergence, probabilistic model checking |
| JEL: | C62 C63 C71 C78 |
| Date: | 2011–07 |
| URL: | http://d.repec.org/n?u=RePEc:has:discpr:1132&r=gth |
| By: | Sandro Casal (School of Social Sciences, University of Trento); Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); Mofei Jia (School of Social Sciences, University of Trento); Matteo Ploner (DECO-CEEL, University of Trento) |
| Abstract: | Envy is often the cause of mutually harmful outcomes. We experimentally study the impact of envy in a bargaining setting in which there is no conflict in material interests: a proposer, holding the role of residual claimant, chooses the size of the pie to be shared with a responder, whose share is exogenously fixed. Responders can accept or reject the proposal, with game types differing in the consequences of rejection: all four combinations of (not) self-harming and (not) other-harming are considered. We find that envy leads responders to reject high proposer claims, especially when rejection harms the proposer. Notwithstanding, maximal claims by proposers are predominant for all game types. This generates conflict and results in a considerable loss of efficiency. |
| Keywords: | Social Preferences, Conflict, Experimental Economic,, Bargaining |
| JEL: | D63 D74 C91 C72 |
| Date: | 2011–11–04 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2011-051&r=gth |
| By: | Agnes Bäker (University of Tübingen, Department of Business and Economics); Werner Güth (Max Planck Institute of Economics, Strategic Interaction Group); Kerstin Pull (University of Tübingen, Department of Business and Economics); Manfred Stadler (University of Tübingen, Department of Business and Economics) |
| Abstract: | nnovative behavior is mostly studied theoretically, e.g., in models of patent races, and empirically, e.g., by using R&D or patent data. This research, however, is only poorly informed about the psychological tradition of creativity research. Our study is an attempt to experimentally collect behavioral data revealing in how far creativity, analytical skills, personality traits and innovation game behavior in the lab are interrelated. With the help of a within-subject design we find that participants' performance in the innovation games is in fact related to their creativity, risk tolerance and self-control. Other personality traits such participants' anxiety, independence, tough-mindedness and extraversion, if any, only play a minor role, and the same is true for participants' analytical skills. |
| Keywords: | Creativity, personality traits, innovation games, experiments |
| JEL: | C91 L13 O31 |
| Date: | 2011–11–09 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2011-056&r=gth |
| By: | Timothy C. Salmon; Roberto A. Weber |
| Abstract: | Efficient growth often requires the integration of individuals from lower-performing groups, firms, or societies into higher-performing ones. Such integration may be difficult without facilitating interventions or restrictions. We explore, using a laboratory experiment, the effectiveness of two regularly-employed entry restrictions: entry quotas and entry exams. We use a coordination game with Pareto-ranked equilibria, in which we allow an efficiently-coordinated group and an inefficiently-coordinated one to arise endogenously. We then allow individuals to move from the low-performing group to the high-performing one. We vary whether such movement is unrestricted, is limited to one entrant per period, or is subject to passing an entry exam. We find both kinds of restrictions improve the efficient integration of entrants, but that there is no additional benefit obtained by their combination. The restrictions lead to improved behavior among entrants, but they have a stronger influence on the maintenance of good behavior among incumbents in the high-performing group. |
| Keywords: | Growth, entry, coordination, experiments |
| JEL: | C72 C92 M12 |
| Date: | 2011–10 |
| URL: | http://d.repec.org/n?u=RePEc:zur:econwp:035&r=gth |
| By: | Etienne Billette de Villemeur (EQUIPPE, Université de Lille, Villeneuve dAscq F-59655, France); Richard Ruble (Université de Lyon, Lyon F-69007, France; EMLYON Business School, Ecully F-69134 & CNRS, GATE Lyon Saint Etienne, Ecully F-69130, France); Bruno Versaevel (Université de Lyon, Lyon F-69007, France; EMLYON Business School, Ecully F-69134 & CNRS, GATE Lyon Saint Etienne, Ecully F-69130, France) |
| Abstract: | We characterize sequential (preemption) and simultaneous (coordination) equilibria, as well as joint-value maximizing (cooperation) solutions, in a model of investment timing allowing for externalities in both flow pro…ts and investment costs. For two ex-ante symmetric …rms, either preemption or attrition occur depending on the size of the investment externality. Coordination is less likely with more discounting, as in a repeated game, and more likely with higher growth and volatility. Optimal cooperation involves either monopoly or duopoly investment, the latter being either symmetric or asymmetric. Finally, these characterizations are validated by applications to standard speci…cations of capacity accumulation and of R&D investment. In the former setup, coordination is likelier if installed capacities and lumpy investments are both large. With R&D input choices, if investment synergies are large, coordination and cooperation result in the same outcomes. |
| Keywords: | Investment Timing, Real Options, Simultaneous Equilibrium, Joint-Value Maximization, Cooperation, Investment Externalities |
| JEL: | C73 D43 D92 L13 |
| Date: | 2011 |
| URL: | http://d.repec.org/n?u=RePEc:gat:wpaper:1128&r=gth |