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on Game Theory |
| By: | Andrew McLennan (School of Economics, The University of Queensland); Rabee Tourky (School of Economics, The University of Queensland) |
| Abstract: | TAn imitation game is a finite two person normal form game in which the two players have the same set of pure strategies and the goal of the second player is to choose the same pure strategy as the first player. Gale et al. (1950) gave a way of passing from a given two person game to a symmetric game whose symmetric Nash equilibria are in oneto-one correspondence with the Nash equilibria of the given game. We give a way of passing from a given symmetric two person game to an imitation game whose Nash equilibria are in one-to-one correspondence with the symmetric Nash equilibria of the given symmetric game. Lemke (1965) portrayed the Lemke-Howson algorithm as a special case of the Lemke paths algorithm. Using imitation games, we show how Lemke paths may be obtained by projecting Lemke-Howson paths. |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:qld:uq2004:359&r=gth |
| By: | Béal, Sylvain (Sonderforschungsbereich 504); Durieu, Jacques (CREUSET, University of Saint-Etienne); Solal, Philippe (CREUSET, University of Saint-Etienne) |
| Abstract: | We study farsighted coalitional stability in the context of TUgames. Chwe (1994, p.318) notes that, in this context, it is difficult to prove nonemptiness of the largest consistent set. We show that every TU-game has a nonempty largest consistent set. Moreover, the proof of this result points out that each TU-game has a farsighted stable set. We go further by providing a characterization of the collection of farsighted stable sets in TU-games. We also show that the farsighted core of a TU-game is empty or is equal to the set of imputations of the game. Next, the relationships between the core and the largest consistent set are studied in superadditive TU-games and in clan games. In the last section, we explore the stability of the Shapley value. It is proved that the Shapley value of a superadditive TU-game is always a stable imputation: it is a core imputation or it constitutes a farsighted stable set. A necessary and sufficient condition for a superadditive TU-game to have the Shapley value in the largest consistent set is given. |
| Date: | 2007–08–06 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:sfbmaa:07-57&r=gth |
| By: | Berninghaus, Siegfried K. (Universität Karlsruhe); Ehrhart, Karl-Martin (Universitaet Karlsruhe); Ott, Marion (Universitaet Karlsruhe) |
| Abstract: | A population of players is considered in which each agent can select her neighbors in order to play a 2x2 Hawk-Dove game with each of them. We design our experiment in continuous time where participants may change their Hawk-Dove action and/or their neighborhood at any point in time. We are interested in the resulting formation of networks and the action distributions. Compared with static Nash equilibrium (e.g., Berninghaus and Vogt, 2004, 2006; Bramoulle, Lopez-Pintado, Goyal, and Vega-Redondo, 2004) and social optimum as theoretical benchmark solutions, subjects seem to employ a more complex, forward-looking thinking. We develop an other benchmark solution, called one-step-ahead stability, that combines forward-looking belief formation with rational response and that fits the data much better. |
| Date: | 2008–01–31 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:sfbmaa:08-02&r=gth |
| By: | Abele, Susanne (Miami University, Department of Psychology); Stasser, Garold (Miami University, Department of Psychology) |
| Abstract: | Conflicts between individuals’ and collective interests are ubiquitous in social life. Numerous experimental studies have investigated the resolution of such conflicts using public good games with either continuous or step-level payoff functions. A conceptual analysis using both classic game theory and social exchange theory shows that these two types of games are fundamentally different. A continuous function game is a social dilemma in that it contains a conflict between individual and collective interests whereas a step-level game is primarily a social coordination game. Thus, we conclude that one can not safely generalize results from step-level to continuous form games. Additionally, our analysis shows that the distinction between continuous and single-step games can be blurred by segmenting a continuous function into steps or adding steps to a single-step game. We identify characteristics of the payoff function that conceptually mark the transition from a dilemma to a coordination problem. |
| Date: | 2007–12–17 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:sfbmaa:07-72&r=gth |
| By: | Eichberger, Jürgen (Sonderforschungsbereich 504); Kelsey, David (Department of Economics, The University of Birmingham); Schipper, Burkhard (University of California, Davis Department of Economics) |
| Abstract: | We present a non-technical account of ambiguity in strategic games and show how it may be applied to economics and social sciences. Optimistic and pessimistic responses to ambiguity are formally modelled. We show that pessimism has the effect of increasing (decreasing)equilibrium prices under Cournot (Bertrand) competition. In addition the effects of ambiguity on peace-making are examined. It is shown that ambiguity may select equilibria in coordination games with multiple equilibria. Some comparative statics results are derived for the impact of ambiguity in games with strategic complements. |
| Date: | 2007–06–20 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:sfbmaa:07-19&r=gth |
| By: | Damianov, Damian S. (The University of Texas-Pan American); Oechssler, Jörg (Department of Economics, University of Heidelberg); Becker, Johannes Gerd (ETH Zurich, Department of Economics) |
| Abstract: | In the variable supply auction considered here, the seller decides how many costumers with unit demand to serve after observing their bids. Bidders are uncertain about the seller's cost. We experimentally investigate whether a uniform or a discriminatory price auction is better for the seller in this setting. Exactly as predicted by theory, it turns out that the uniform price auction produces substantially higher bids, and consequently yields higher revenues and profits for the seller. Somewhat surprisingly but again predicted by theory, it also yields a higher number of transactions, which makes it the more efficient auction format. |
| Date: | 2007–12–05 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:sfbmaa:07-68&r=gth |
| By: | Jeanne Hagenbach; Frédéric Koessler |
| Abstract: | In this paper, we consider situations in which individuals want to choose an action close to others' actions as well as close to a payoff relevant state of nature with the ideal proximity to the common state varying across the agents. Before this coordination game with heterogeneous preferences is played, a cheap talk communication stage is offered to players who decide to whom they reveal the private information they hold about the state. The strategic information transmission taking place in the communication stage is characterized by a "strategic communication network". We provide a direct link between players' preferences and the strategic communication network emerging at equilibrium, depending on the strength of the coordination motive and the prior information structure. Equilibrium strategic communication networks are characterized in a very tractable way and compared in term of efficiency. In general, a maximal strategic communication network may not exist and communication networks cannot be ordered in the sense of Pareto. However, expected social welfare always increases when the communication network expands. Strategic information transmission can be improved when group or public communication is allowed, and/or when information is certifiable. |
| Date: | 2008 |
| URL: | http://d.repec.org/n?u=RePEc:pse:psecon:2008-10&r=gth |
| By: | Meffert, Michael F. (Sonderforschungsbereich 504); Gschwend, Thomas (Sonderforschungsbereich 504) |
| Abstract: | The theory of strategic voting has been tested in experiments for elections in single member districts with three candidates or parties. It is unclear whether it can explain strategic voting behavior in a fairly common type of political system, multi-party systems with proportional representation, minimum vote thresholds, and coalition governments. In this paper, we develop a (non-formal) strategic voting game and show in a simulation that the model produces election scenarios and outcomes with desirable characteristics. We then test the decision-theoretic model in a laboratory experiment. Participants with a purely instrumental (financial) motivation voted in a series of 25 independent elections. The availability of polls and coalition signals by parties was manipulated. The results show that voters are frequently able to make optimal or strategic vote decisions, but that voters also rely on simple decision heuristics and are highly susceptible to coalition signals by parties. |
| Date: | 2007–07–30 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:sfbmaa:07-55&r=gth |
| By: | Rene van den Brink (VU University Amsterdam); Yukihiko Funaki (Wasdeda University Tokyo); Gererd van der Laan (VU University Amsterdam) |
| Abstract: | We introduce a new solution for bankruptcy problems that satisfies weaker versions of the Exemption en Exclusion properties from the literature. Although the principles of Exclusion and Exemption are appealing, the specific conditions under which an agent receives its claim, respectively nothing, seem arbitrary and are inconsistent in the sense that there is no bankruptcy rule that satisfies both. However, weakening these conditions (by putting lower boundaries on what is considered to be a ‘small claim’), there do exist rules satisfying both principles. In this paper we consider a Weak Exemption and a Weak Exclusion property such that there is a unique bankruptcy rule that satisfies these two properties together with Consistency and Weak Proportionality (i.e. a change in the estate effects the payoffs of agents with bigger claims more than the payoffs of agents with smaller claims). This rule turns out to be some kind of reverse of the famous Talmud rule. Moreover, we show that Weak Exemption and Weak Exclusion are each others dual, and that the Reverse Talmud rule also can be characterized as the unique Self-Dual solution that satisfies Weak Proportionality and either Weak Exemption or Weak Exclusion. Finally, we generalize the Reverse Talmud rule to a class of bankruptcy rules that all satisfy some Weak Exemption and some Weak Exclusion property (that are not necessarily each others dual), which contains the famous Constrained Equal Awards and Constrained Equal Losses rules as extreme cases. |
| Keywords: | Bankruptcy problem; Exemption; Exclusion; Self-Duality; Talmud rule; Reverse Talmud Rule |
| JEL: | D63 |
| Date: | 2008–03–07 |
| URL: | http://d.repec.org/n?u=RePEc:dgr:uvatin:20080026&r=gth |
| By: | Philippe Bich (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I) |
| Abstract: | One answers to an open question of Herings et al. (2008), by proving that their fixed point theorem for discontinuous functions works for mappings defined on convex compact subset of $\R^n$, and not only polytopes. This fixed point theorem can be applied to the problem of Nash equilibrium existence in discontinuous games. |
| Keywords: | fixed point theorem; discontinuity; nash equilibrium |
| Date: | 2008–02 |
| URL: | http://d.repec.org/n?u=RePEc:hal:papers:halshs-00265464_v1&r=gth |
| By: | Dürsch, Peter (Department of Economics, University of Heidelberg); Servátka, Maros (Department of Economics, University of Canterbury) |
| Abstract: | We conduct a prisoner’s dilemma experiment with a punishment/reward stage, where punishments and rewards are risky. This is compared with a risk free treatment. We find that subjects do not change their behavior in the face of risky outcomes. Additionally, we measure risk attitude and the emotions of subjects. While we find a strong influence of emotions, individual risk aversion has no effect on the decision to punish or reward. This is good news for lab experiments who abstract from risky outcomes. From the perspective of social preferences, our results provide evidence for risk neutral inclusion of other player’s payoffs in the decisionmaker’s utility function. |
| Date: | 2007–09–05 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:sfbmaa:07-62&r=gth |
| By: | Meffert, Michael F. (Sonderforschungsbereich 504); Gschwend, Thomas (Sonderforschungsbereich 504) |
| Abstract: | Coalition governments are the norm in many countries, even though voters can only cast their vote for an individual party, not a specific coalition. Some voters might nevertheless cast their vote in a way that maximizes the probability that a preferred coalition will be formed after the election. In the paper, we investigate the effect of coalition preferences and expectations on vote decisions, above and beyond the preferences for specific parties. We focus in particular on voters’ ability to form differentiated expectations about possible coalitions, the likelihood of a majority and the likelihood that the parties will be able to agree on a coalition. We report the results of a nationally representative survey conducted before the 2006 Austrian General Election. We collected detailed information about respondents' party and coalition preferences and expectations about the electoral outcomes. Green Party voters are used to demonstrate that the effect of coalition preferences depends on whether or not voters expect a coalition to succeed. |
| Date: | 2007–10–23 |
| URL: | http://d.repec.org/n?u=RePEc:xrs:sfbmaa:07-64&r=gth |
| By: | Luis C. Corchon |
| Date: | 2007–12 |
| URL: | http://d.repec.org/n?u=RePEc:cte:werepe:we081207&r=gth |