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on Game Theory |
| By: | Koji Yokote (Graduate School of Economics, Waseda University); Yukihiko Funaki (Faculty of Political Science and Economics, Waseda University) |
| Abstract: | We introduce several bases of the set of TU games. Given a coalition T, Yokote et al. (2013) introduced the commander game in which a coalition including 1 player in T obtains payoff. On the other hand, Shapley (1953) introduced the unanimity game in which a coalition including all players in T obtains payoff. We consider the intermediate between the two games. We introduce a game in which a coalition including k players in T obtains payoff, where 1 ≤ k ≤| T |. We show that, if there is a specific relationship between the size of coalition T and k, we can construct a new basis. By using the new basis, we give sufficient conditions under which the Shapley value coincides with the prenucleolus. |
| Keywords: | basis; Shapley value; prenucleolus; coincidence condition |
| JEL: | C71 |
| Date: | 2015–01 |
| URL: | http://d.repec.org/n?u=RePEc:wap:wpaper:1419&r=gth |
| By: | Christoph Kuzmics (Center for Mathematical Economics, Bielefeld University); Daniel Rodenburger (University of Jena) |
| Abstract: | Using data from an experiment by Forsythe, Myerson, Rietz, and Weber (1993), designed for a different purpose, we test the "standard theory" that players have preferences only over their own mentary payoffs and that play will be in (evolutionary stable) equilibrium. In the experiment each subject is recurrently (24 times) randomly matched with ever changing opponents to play a 14 player game. We find that assuming risk-neutrality for all players leads to a predicted evolutionary stable equilibrium that, while it can be rejected at the 5% level of significance, is nevertheless remarkably close to "explaining" the data. Moreover, when we assume that players are risk-averse and we calibrate their risk-aversion in one treatment with a simple game, this theory cannot be rejected at the 5% level of significance for another treatment with a more complicated game, despite the fact that we have close to 400 data points. |
| Keywords: | opinion polls, elections, voting, testing, Nash equilibrium, attainable equilibrium, symmetries |
| JEL: | C72 D72 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:bie:wpaper:542&r=gth |
| By: | de Haan, Monique (University of Oslo); Gautier, Pieter A. (VU University Amsterdam); Oosterbeek, Hessel (University of Amsterdam); van der Klaauw, Bas (VU University Amsterdam) |
| Abstract: | Theory points to a potential trade-off between two main school assignment mechanisms; Boston and Deferred Acceptance (DA). While DA is strategy-proof and gives a stable matching, Boston might outperform DA in terms of ex-ante efficiency. We quantify the (dis)advantages of the mechanisms by using information about actual choices under Boston complemented with survey data eliciting students' school preferences. We find that under Boston around 8% of the students apply to another school than their most-preferred school. We compare allocations resulting from Boston with DA with single tie-breaking (one central lottery; DA-STB) and multiple tie-breaking (separate lottery per school; DA-MTB). DA-STB places more students in their top-n schools, for any n, than Boston and results in higher average welfare. We find a trade-off between DA-STB and DA-MTB. DA-STB places more students in their single most-preferred school than DA-MTB, but fewer in their top-n, for n ≥ 2. Finally, students from disadvantaged backgrounds benefit most from a switch from Boston to any of the DA mechanisms. |
| Keywords: | school choice, Boston mechanism, deferred acceptance mechanism, strategic behavior, ex-ante efficiency, ex-post efficiency |
| JEL: | C83 I20 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp9118&r=gth |
| By: | Seungjin Han |
| Abstract: | This paper studies competing mechanism problems in directed search markets in which multiple principals (e.g., sellers) simultaneously offer trading mechanisms to multiple agents (e.g., buyers) to compete for trading opportunities, and agents select any particular principal for trading via directed search. A principal's mechanism can be sufficiently general to make his terms of trade contingent on agents' messages, which may reflect not only their types but also changes in others' terms of trade. This paper is interested in an equilibrium with dominant strategy implementable punishment (DSIP) where principals punish the deviating principal with dominant strategy incentive compatible (DIC) direct mechanisms when a principal's deviation becomes evident from agents' messages. This DIC property of punishment off the path makes equilibrium analysis tractable. This paper provides the greatest lower bound of a principal's payoff supportable in an equilibrium with DSIP in terms of incentive compatible direct mechanisms. It also provides implications of the results. |
| Keywords: | click stream pricing, on-line markets, competing mechanisms, market information, implicit collusion, robust equilibrium |
| JEL: | C72 D82 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:mcm:deptwp:2015-07&r=gth |
| By: | Stefan Rass |
| Abstract: | Optimal behavior in (competitive) situation is traditionally determined with the help of utility functions that measure the payoff of different actions. Given an ordering on the space of revenues (payoffs), the classical axiomatic approach of von Neumann and Morgenstern establishes the existence of suitable utility functions, and yields to game-theory as the most prominent materialization of a theory to determine optimal behavior. Although this appears to be a most natural approach to risk management too, applications in critical infrastructures often violate the implicit assumption of actions leading to deterministic consequences. In that sense, the gameplay in a critical infrastructure risk control competition is intrinsically random in the sense of actions having uncertain consequences. Mathematically, this takes us to utility functions that are probability-distribution-valued, in which case we loose the canonic (in fact every possible) ordering on the space of payoffs, and the original techniques of von Neumann and Morgenstern no longer apply. This work introduces a new kind of game in which uncertainty applies to the payoff functions rather than the player's actions (a setting that has been widely studied in the literature, yielding to celebrated notions like the trembling hands equilibrium or the purification theorem). In detail, we show how to fix the non-existence of a (canonic) ordering on the space of probability distributions by only mildly restricting the full set to a subset that can be totally ordered. Our vehicle to define the ordering and establish basic game-theory is non-standard analysis and hyperreal numbers. |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1506.07368&r=gth |
| By: | Lorenzo Cerda Planas (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics) |
| Abstract: | The aim of this paper is twofold. Starting from the population dynamics literature, which usually finds the resulting distribution of a trait in a population, according to some parents' preferences, I answer the inverted question: Which preference function would yield into a given trait distribution? I solve this using a continuous trait, instead of finite types of agents. Using this result, I connect this transmission theory of social traits with the well-known results of Dictator Game (DG) experiments. I use a specific definition of a Kantian trait applied to DG results, and determine the distribution of this trait that is commonly found in these experiments. With these two ingredients, I show that homo-œconomicus parents have a greater' dislike' or disutility of having offspring with different traits from them compared to their Kantian counterparts. This could be a result of myopic empathy being stronger in homo-œconomicus parents, driving this dislike of difference. |
| Date: | 2015–03 |
| URL: | http://d.repec.org/n?u=RePEc:hal:cesptp:halshs-01163937&r=gth |
| By: | Tsuyoshi Toshimitsu (School of Economics, Kwansei Gakuin University) |
| Abstract: | We consider endogenous choice of the strategic variables, price and quantity, in a horizontally differentiated duopoly market, assuming network effects and product compatibility (hereafter, network compatibility effects). We demonstrate the following. If the degree of network compatibility effects of the other rival firm is smaller (larger) than the degree of product substitutability, then choosing quantity (price) is a dominant strategy for the firm. In this case, the Cournot (Bertrand) equilibrium arises. If there are asymmetric network compatibility effects between the firms, the firm with larger (smaller) network compatibility effects than the degree of product substitutability chooses quantity (price). In this case, the Cournot−Bertrand equilibrium arises. |
| Keywords: | Bertrand equilibrium; Cournot equilibrium; Cournot−Bertrand equilibrium; product compatibility; network effect; fulfilled expectation; horizontally differentiated duopoly |
| JEL: | C72 D01 D43 L13 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:kgu:wpaper:128&r=gth |