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on Game Theory |
| By: | Rene van den Brink (Department of Econometrics and Tinbergen Institute, Faculty of Economics and Business Administration, Free University Amsterdam); Rene Levinsky (Max Planck Institute of Economics); Miroslav Zeleny (Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Czech Republic) |
| Abstract: | The Shapley value of a cooperative transferable utility game distributes the dividend of each coalition in the game equally among its members. Given exogenous weights for all players, the corresponding weighted Shapley value distributes the dividends proportionally to their weights. In this contribution we deï¬ne the balanced solution which assigns weights to players such that the corresponding weighted Shapley value of each player is equal to her weight. We prove its existence for all monotone transferable utility games, discuss other properties of this solution, and deal with its characterization through a reduced game consistency. |
| Keywords: | Balanced solution, Proportionality, Reduced game consistency, Weighted Shapley value. |
| JEL: | C71 |
| Date: | 2007–10–15 |
| URL: | http://d.repec.org/n?u=RePEc:jrp:jrpwrp:2007-073&r=gth |
| By: | Thierry Vignolo |
| Abstract: | This paper investigates imitation and selective matching in reputational games with an outside option. We identify two classes of such games, which are ultimatum and trust games. By selective matching we mean that short-runplayers have the possibility of selecting the long-run player they play against. We find that selective matching (unlike random matching) favors the equilibrium associated to reputation in the ultimatum game but not in the trust game. |
| Keywords: | Reputation; Long-run equilibria; Selective matching; Games with an outside option |
| JEL: | C72 C73 L1 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2007/31&r=gth |
| By: | Azrieli, Yaron |
| Abstract: | We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player is a best response to the distribution of actions of his opponents in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game. |
| Keywords: | Random-matching game; Categorization; Correlated equilibrium |
| JEL: | D82 C72 |
| Date: | 2007–10–25 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:5475&r=gth |
| By: | Noemí NAVARRO; Róbert VESZTEG |
| Abstract: | We conduct a laboratory experiment to test the empirical behavior of the bid-and-propose mechanism, defined in Navarro and Perea (2005). This mechanism implements the Myerson value for networks, and therefore its outcome posesses fairness properties. Since the bid-and-propose mechanism includes an ultimatum game in the last stage, we design an experiment with several treatments, where subjects also play the simple ultimatum game. In order to check whether subjectsbehave fairly in the sense of Myerson or they are inequity averse, we compare resultsfrom games with symmetric and asymmetric outside options. |
| Keywords: | experiments; fairness; Myerson value; ultimatum game |
| JEL: | C72 C91 D63 |
| Date: | 2007–08 |
| URL: | http://d.repec.org/n?u=RePEc:lau:crdeep:07.05&r=gth |
| By: | Luisa Carente; Balbina Casas-Mendez; Ignacio Carcia-Jurado; Anne van den Nouweland |
| Abstract: | We define and study games with limited aspirations. In a game with limited aspirations there are upper bounds on the possible payoffs for some coalitions. These restrictions require adjustments in the definitions of solution concepts. In the current paper we study the effect of the restrictions on the core and define and study the so-called truncated core. |
| Keywords: | games with limited aspirations, truncated core. |
| JEL: | C71 C44 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:mlb:wpaper:1010&r=gth |
| By: | Ed Hopkins |
| Abstract: | A new method is proposed for the analysis of first price and all pay auctions, where bidding functions are written not as functions of values but as functions of the rank or quantile of the bidder’s value in the distribution from which it was drawn. This method gives new results in both symmetric and asymmetric cases with independent values. It is shown that under this new method if one bidder has a stochastically higher distribution of values then her bidding function in terms of rank will always be higher than her rival’s. This is a clearer result under weaker conditions than using standard methods. We also look at auctions where one bidder has more precise information than the other. |
| Keywords: | : first price auctions, all pay auctions, comparative statics, games of incomplete information, stochastic dominance, rank, quantile. |
| JEL: | C72 D44 D82 |
| Date: | 2007–10–15 |
| URL: | http://d.repec.org/n?u=RePEc:edn:esedps:173&r=gth |
| By: | Alejandro Saporiti (School of Social Sciences, University of Manchester, Arthur Lewis Building, M13 9PL Manchester, United Kingdom) |
| Abstract: | This paper analyzes collective choices in a society with strategic voters and single-crossing preferences. It shows that, in addition to single-peakedness, single-crossingness is another meaningful domain which guarantees the existence of non-manipulable social choice functions. A social choice function is shown to be anonymous, unanimous and strategy-proof on single-crossing domains if and only if it is an extended median rule with n-1 parameters distributed on the end points of the feasible set of alternatives. Such rules are known as positional dictators, and they include the median choice rule as a particular case. As a by-product, the paper also provides an strategic foundation for the so called "single-crossing version" of the Median Voter Theorem, by showing that the median ideal point can be implemented in dominant strategies through a simple mechanism in which each agent honestly reveals his preferences. |
| Keywords: | Strategy-proofness; single-crossing; median voter; positional dictators |
| JEL: | D70 D71 |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:roc:wallis:wp48&r=gth |
| By: | John Smith (Rutgers University-Camden) |
| Abstract: | We interpret the psychology literature on social identity and examine its implications in a population partially composed of such agents. We model a population of agents from two exogenous and well defined social groups. Agents are randomly matched to play a reduced form bargaining game. We show that this struggle for resources drives a conflict through the rational destruction of surplus. We assume that the population contains both rational players and behavioral players. Behavioral players aggressively discriminate against members of the other social group. The existence and specification of the behavioral player is motivated by the social identity literature. For rational players, group membership has no payoff relevant consequences. We show that rational players can contribute to the conflict by aggressively discriminating and that this behavior is consistent with existing empirical evidence. Our paper relates to the empirical literature which finds that our measure of social heterogeneity tends to be increasing in economic variables which we interpret as signifying inefficiency. We provide an explanation that, as social groups compete for the benefits of public goods, disagreement and inefficiency can result. Our work also relates to the social conflict literature, which examines the relationship between macro level factors such as unemployment and civil disturbances. This literature finds that the amount of social conflict tends to be increasing in what we refer to as the inequitability of the environment. |
| Keywords: | reputation, conflict, identity |
| JEL: | C72 D74 L14 |
| Date: | 2007–10–14 |
| URL: | http://d.repec.org/n?u=RePEc:rut:rutres:200709&r=gth |
| By: | Antonella Ianni |
| Abstract: | This paper studies the analytical properties of the reinforcement learning model proposed in Erev and Roth (1998), also termed cumulative reinforcement learning in Laslier et al. (2001). The stochastic model of learning accounts for two main elements: the Law of Effect (positive reinforcement of actions that perform well) and the Power Law of Practice (learning curves tend to be steeper initially). The paper establishes a relation between the learning process and the underlying deterministic replicator equation. The main results show that if the solution trajectories of the latter converge su¢ ciently fast, then the probability that all the realizations of the learning process over a given spell of time, possibly infinite, becomes arbitrarily close to one, from some time on. In particular, the paper shows that the property of fast convergence is always satisfied in proximity of a strict Nash equilibrium. The results also provide an explicit estimate of the approximation error that could prove to be useful in empirical analysis. |
| JEL: | C72 C92 D83 |
| Date: | 2007 |
| URL: | http://d.repec.org/n?u=RePEc:eui:euiwps:eco2007/21&r=gth |
| By: | Hitoshi Matsushima (Faculty of Economics, University of Tokyo) |
| Abstract: | This paper incorporates behavioral economics into implementation theory. We use mechanisms that are strictly detail-free. We assume that each agent dislikes telling a white lie when such lying does not serve her/his material interest. We present a permissive result wherein by using just a single detail-free mechanism, any alternative can be uniquely implemented in iterative dominance as long as the agents regard this alternative as being socially desirable. |
| Date: | 2007–10 |
| URL: | http://d.repec.org/n?u=RePEc:tky:fseres:2007cf523&r=gth |
| By: | Ben Greiner; Axel Ockenfels; Peter Werner |
| Abstract: | We study the interplay of inequality and trust in a dynamic game, where trust increases efficiency and thus allows higher growth of the experimental economy in the future. We find that trust is initially high in a treatment starting with equal endowments, but decreases over time. In a treatment with unequal endowments, trust is initially lower yet remains relatively stable. The difference seems partly due to the fact that equal start positions increase subjects’ inclination to condition their trust decisions on wealth comparisons, whereas conditional trust is much less prevalent with unequal initial endowments. As a result, with respect to efficiency, the initially more unequal economy fares worse in the short run but better in the long run, and the disparity of wealth distributions across economies mitigates over time. |
| Keywords: | inequality, trust, growth, laboratory experiments |
| JEL: | C73 C92 D63 E25 O15 |
| Date: | 2007–10–12 |
| URL: | http://d.repec.org/n?u=RePEc:kls:series:0037&r=gth |
| By: | Matthias Sutter |
| Abstract: | Informational asymmetries abound in economic decision making and often provide an incentive for deception through telling a lie or misrepresenting information. In this paper I use a cheap-talk sender-receiver experiment to show that telling the truth should be classified as deception too if the sender chooses the true message with the expectation that the receiver will not follow the sender’s (true) message. The experimental data reveal a large degree of ‘sophisticated’ deception through telling the truth. The robustness of my broader definition of deception is confirmed in an experimental treatment where teams make decisions. |
| Keywords: | Deception, Expectations, Team decision making, Individual decision making, Experiment |
| JEL: | C72 C91 D82 |
| Date: | 2007–10–23 |
| URL: | http://d.repec.org/n?u=RePEc:inn:wpaper:2007-26&r=gth |
| By: | James Albrecht; Axel Anderson; Susan Vroman (Department of Economics, Georgetown University) |
| Abstract: | We consider the problem of sequential search when the decision to stop searching is made by a committee. We show that a symmetric stationary equilibrium exists and is unique given that the distribution of rewards is log concave. Committee members set a lower acceptance threshold than do single-agent searchers. In addition, mean preserving spreads in the distribution of rewards may lower each member's continuation value | an impossibility in the single-agent setting. If committee members are very patient or very impatient, expected search duration is lower than it would be for a single agent, but, for intermediate levels of patience, this comparison may be reversed. Holding the fraction of votes required to stop fixed, expected search duration rises with committee size on patient committees but falls with committee size on impatient committees. Finally, we consider the effect of varying the number of votes required to stop, holding committee size constant. We show that the welfare-maximizing vote threshold increases in the rate of patience and that there is a finite bound on patience such that unanimity is welfare maximizing. Classification-JEL Codes: D71, D72, D83 |
| Keywords: | sequential search, voting, committees |
| Date: | 2007–07–09 |
| URL: | http://d.repec.org/n?u=RePEc:geo:guwopa:gueconwpa~07-07-09&r=gth |