|
on Game Theory |
| By: | Heller, Yuval; Mohlin, Erik |
| Abstract: | We study environments in which agents from a large population are randomly matched to play a one-shot game, and, before the interaction begins, each agent observes noisy information about the partner's aggregate behavior. Agents follow stationary strategies that depend on the observed signal. We show that every strategy distribution admits a unique behavior if each player observe on average less than action of his partner. On the other hand, if each player observes on average more than one action, we show that there exists a stationary strategy that admits multiple consistent outcomes. |
| Keywords: | Markovian process, Random matching. |
| JEL: | C72 C73 D83 |
| Date: | 2015–08–13 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:66179&r=all |
| By: | Zhou Zhou |
| Abstract: | We consider two-player non-zero-sum stopping games in discrete time. Unlike Dynkin games, in our games the payoff of each player is revealed after both players stop. Moreover, each player can adjust her own stopping strategy according to the other player's action. In the first part of the paper, we consider the game where players act simultaneously at each stage. We show that there exists a Nash equilibrium in mixed stopping strategies. In the second part, we assume that one player has to act first at each stage. In this case, we show the existence of a Nash equilibrium in pure stopping strategies. |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1508.06032&r=all |
| By: | Abito, Jose Miguel |
| Abstract: | I propose a strategy to identify structural parameters in infinitely repeated games without relying on equilibrium selection assumptions. Although Folk theorems tell us that almost any individually rational payoff can be an equilibrium payoff for sufficiently patient players, Folk theorems also provide tools to explicitly characterize this set of payoffs. I exploit the extreme points of this set to bound unobserved equilibrium continuation payoffs and then use these to generate informative bounds on structural parameters. I illustrate the identification strategy using (1) an infinitely repeated Prisoner's dilemma to get bounds on a utility parameter, and (2) an infinitely repeated quantity-setting game to get bounds on marginal cost and provide a robust test of firm conduct. |
| Keywords: | Repeated games, identification, dynamic games, bounds |
| JEL: | C1 C73 L4 |
| Date: | 2015–08–31 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:66378&r=all |
| By: | Brügemann, Björn; Gautier, Pieter A.; Menzio, Guido |
| Abstract: | The paper revisits the problem of wage bargaining between a firm and multiple workers. We show that the Subgame Perfect Equilibrium of the extensive-form game proposed by Stole and Zwiebel (1996a) does not imply a profile of wages and profits that coincides with the Shapley values as claimed in their classic paper. We propose an alternative extensive-form bargaining game, the Rolodex Game, that follows a simple and realistic protocol and that, under some mild restrictions, admits a unique Subgame Perfect Equilibrium generating a profile of wages and profits that are equal to the Shapley values. The vast applied literature that refers to the Stole and Zwiebel game to give a game-theoretic foundation to the use of the Shapley values as the outcome of the bargain between a firm and multiple workers should instead refer to the Rolodex game. |
| Keywords: | intra firm bargaining; Shapley value |
| JEL: | D21 J30 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10794&r=all |
| By: | Björn Brügemann (VU University Amsterdam); Pieter Gautier (VU University Amsterdam); Guido Menzio (University of Pennsylvania, United States) |
| Abstract: | The paper revisits the problem of wage bargaining between a firm and multiple workers. We show that the Subgame Perfect Equilibrium of the extensive-form game proposed by Stole and Zwiebel (1996a) does not imply a profile of wages and profits that coincides with the Shapley values as claimed in their classic paper. We propose an alternative extensive-form bargaining game, the Rolodex Game, that follows a simple and realistic protocol and that, under some mild restrictions, admits a unique Subgame Perfect Equilibrium generating a profile of wages and profits that are equal to the Shapley values. The vast applied literature that refers to the Stole and Zwiebel game to give a game-theoretic foundation to the use of the Shapley values as the outcome of the bargain between a firm and multiple workers should instead refer to the Rolodex game. |
| Keywords: | Intra firm bargaining; Shapley value |
| JEL: | D21 J30 |
| Date: | 2015–08–18 |
| URL: | http://d.repec.org/n?u=RePEc:tin:wpaper:20150100&r=all |
| By: | Björn Brügemann; Pieter Gautier; Guido Menzio |
| Abstract: | The paper revisits the problem of wage bargaining between a firm and multiple workers. We show that the Subgame Perfect Equilibrium of the extensive-form game proposed by Stole and Zwiebel (1996a) does not imply a profile of wages and profits that coincides with the Shapley values as claimed in their classic paper. We propose an alternative extensive-form bargaining game, the Rolodex Game, that follows a simple and realistic protocol and that, under some mild restrictions, admits a unique Subgame Perfect Equilibrium generating a profile of wages and profits that are equal to the Shapley values. The vast applied literature that refers to the Stole and Zwiebel game to give a game-theoretic foundation to the use of the Shapley values as the outcome of the bargain between a firm and multiple workers should instead refer to the Rolodex game. |
| JEL: | D21 J30 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21508&r=all |
| By: | Mike Woodcock; Fernando Uscategui; David Corrales |
| Abstract: | The objective of this paper is to analyze the game of Hex through the use of Game Theory and Graph Theory. Hex is a game where each player must connect two opposite sides by a continuous path of pieces in a hexagonal grid within a rhombus-shaped board. The size of the board is usually 14×14 but the game can be found in a wide range of sizes such as 11×11 and 17×17. Although the strategy is not as deep as in chess, it is still complex, and just like chess, Hex is a no-chance game, and thus it is a perfect candidate to be examined using some formal tools. This game has some interesting features that make it more interesting; unlike chess, the game will never end in a tie, second, the number of possible movements is finite and third, the second player will always win, through this paper, we will show some of these features. |
| Keywords: | Game theory, Hex, Strategy, Hex Theorem, Strategy-stealing |
| JEL: | C72 C65 |
| Date: | 2015–08–05 |
| URL: | http://d.repec.org/n?u=RePEc:col:000176:013417&r=all |
| By: | Jung, Seeun (ESSEC Business School and THEMA); Vranceanu, Radu (ESSEC Business School and THEMA) |
| Abstract: | The paper reports results from an Ultimatum Game experiment with asymmetric information where Proposers can send to Responders misleading information about their endowment. We allow for all possible gender combinations in the Proposer-Responder pairs. Proposer messages that underestimate the actual amount are quite widespread. The frequency of lying is slightly higher in mixed groups. Conditional on lying, men tend to state bigger lies than women. On the other hand, women tend to tell smaller lies when paired with men, than when paired with women. In general, women present higher acceptance rates than men. |
| Keywords: | Gender studies; Ultimatum Game; Asymmetric information; Lies; Extensive vs. intensive margin |
| JEL: | C72 C91 D83 J16 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:ebg:essewp:dr-15014&r=all |
| By: | Bergemann, Dirk; Brooks, Benjamin A; Morris, Stephen |
| Abstract: | This paper explores the consequences of information in sealed bid first price auctions. For a given symmetric and arbitrarily correlated prior distribution over valuations, we characterize the set of possible outcomes that can arise in a Bayesian equilibrium for some information structure. In particular, we characterize maximum and minimum revenue across all information structures when bidders may not know their own values, and maximum revenue when they do know their values. Revenue is maximized when buyers know who has the highest valuation, but the highest valuation buyer has partial information about others’ values. Revenue is minimized when buyers are uncertain about whether they will win or lose and incentive constraints are binding for all upward bid deviations. We provide further analytic results on possible welfare outcomes and report computational methods which work when we do not have analytic solutions. Many of our results generalize to asymmetric value distributions. We apply these results to study how entry fees and reserve prices impact the welfare bounds. |
| Keywords: | Bayes correlated equilibrium; common values; first price auctions; information structure; interdependent values; private values; revenue; welfare bounds |
| JEL: | C72 D44 D82 D83 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10792&r=all |
| By: | Bergemann, Dirk; Heumann, Tibor; Morris, Stephen |
| Abstract: | We analyze demand function competition with a finite number of agents and private information. We show that the nature of the private information determines the market power of the agents and thus price and volume of equilibrium trade. We provide a characterization of the set of all joint distributions over demands and payoff states that can arise in equilibrium under any information structure. In demand function competition, the agents condition their demand on the endogenous information contained in the price. We compare the set of feasible outcomes under demand function to the feasible outcomes under Cournot competition. We find that the first and second moments of the equilibrium distribution respond very differently to the private information of the agents under these two market structures. The first moment of the equilibrium demand, the average demand, is more sensitive to the nature of the private information in demand function competition, reflecting the strategic impact of private information. By contrast, the second moments are less sensitive to the private information, reflecting the common conditioning on the price among the agents. |
| Keywords: | Bayes correlated equilibrium; demand function competition; incomplete information; linear best responses; market power; moment restrictions; price impact; quadratic payoffs; supply function competition; volatility |
| JEL: | C72 C73 D43 D83 G12 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:cpr:ceprdp:10791&r=all |
| By: | Kotowski, Maciej H. (Harvard University) |
| Abstract: | We introduce a new stability concept for multi-period matching markets. Robust prescient stability asserts that agents exhibit foresight concerning how a market can develop in the future, but they retain ambiguity concerning how the market will develop. We show that a robustly presciently stable matching exists for any configuration of agents' preferences. |
| JEL: | C71 C78 D90 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:harjfk:rwp15-042&r=all |
| By: | Kadam, Sangram V. (Harvard University); Kotowski, Maciej H. (Harvard University) |
| Abstract: | We analyze a T-period, bilateral matching economy without monetary transfers. Under natural restrictions on agents' preferences, which accommodate switching costs, status-quo bias, and other forms of inter-temporal complementarity, dynamically stable matchings exist. We propose an ordering of the set of dynamically stable matchings ensuring this set forms a lattice. We investigate the robustness of dynamically stable matchings with respect to the market's time horizon. We relate our analysis to market-design applications, including student-school assignment and labor markets. |
| JEL: | C71 C78 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:harjfk:rwp15-031&r=all |
| By: | Daron Acemoglu; Alexander Wolitzky |
| Abstract: | We introduce the possibility of direct punishment by specialized enforcers into a model of community enforcement. Specialized enforcers need to be given incentives to carry out costly punishments. Our main result shows that, when the specialized enforcement technology is sufficiently effective, cooperation is best sustained by a “single enforcer punishment equilibrium,” where any deviation by a regular agent is punished only once, and only by enforcers. In contrast, enforcers themselves are disciplined (at least in part) by community enforcement. The reason why there is no community enforcement following deviations by regular agent is that such actions, by reducing future cooperation, would decrease the amount of punishment that enforcers are willing to impose on deviators. Conversely, when the specialized enforcement technology is ineffective, optimal equilibria do punish deviations by regular agents with community enforcement. The model thus predicts that societies with more advanced enforcement technologies should rely on specialized enforcement, while less technologically advanced societies should rely on community enforcement. Our results hold both under perfect monitoring of actions and under various types of private monitoring. |
| JEL: | C73 D72 D74 |
| Date: | 2015–08 |
| URL: | http://d.repec.org/n?u=RePEc:nbr:nberwo:21457&r=all |
| By: | GUIMARAES, Bernardo; PEREIRA, Ana Elisa |
| Abstract: | We study a dynamic model of coordination with timing frictions and payoff heterogeneity. There is a unique equilibrium, characterized by thresholds that determine the choices of each type of agent. We characterize equilibrium for the limiting cases of vanishing timing frictions and vanishing shocks to fundamentals. A lot of conformity emerges: despite payoff heterogeneity, agents’ equilibrium thresholds partially coincide as long as there exists a set of beliefs that would make this coincidence possible – though they never fully coincide. In case of vanishing frictions, the economy behaves almost as if all agents were equal to an average type. Conformity is not inefficient. The efficient solution would have agents following others even more often and giving less importance to the fundamental |
| Date: | 2015–03–16 |
| URL: | http://d.repec.org/n?u=RePEc:fgv:eesptd:380&r=all |
| By: | Seeun Jung (ESSEC Business School - Essec Business School, Thema, Université de Cergy-Pontoise - THEMA - Théorie économique, modélisation et applications - Université de Cergy Pontoise - CNRS); Radu Vranceanu (Thema, Université de Cergy-Pontoise - THEMA - Théorie économique, modélisation et applications - Université de Cergy Pontoise - CNRS, ESSEC - ESSEC Business School - Essec Business School - Economics Department - Essec Business School) |
| Abstract: | The paper reports results from an Ultimatum Game experiment with asymmetric information where Proposers can send to Responders misleading information about their endowment. We allow for all possible gender combinations in the Proposer-Responder pairs. Proposer messages that underestimate the actual amount are quite widespread. The frequency of lying is slightly higher in mixed groups. Conditional on lying, men tend to state bigger lies than women. On the other hand, women tend to tell smaller lies when paired with men, than when paired with women. In general, women present higher acceptance rates than men. |
| Date: | 2015–07 |
| URL: | http://d.repec.org/n?u=RePEc:hal:wpaper:hal-01184964&r=all |
| By: | Changat, M.; Lekha, D.S.; Mohandas, S.; Mulder, H.M.; Subhamathi, A.R. |
| Abstract: | __Abstract__ A median (antimedian) of a profile of vertices on a graph G is a vertex that minimizes (maximizes) the sum of the distances to the elements in the profile. The median (antimedian) function has as output the set of medians (antimedians) of a profile. It is one of the basic models for the location of a desirable (obnoxious) facility in a network. The median function is well studied. For instance it has been characterized axiomatically by three simple axioms on median graphs. The median function behaves nicely on many classes of graphs. In contrast the antimedian function does not have a nice behavior on most classes. So a nice axiomatic characterization may not be expected. In this paper an axiomatic characterization is obtained for the median and antimedian function on complete graphs minus a matching. |
| Keywords: | median, antimedian, consensus function, consistency, cocktail-party graph, complete graph, consensus axiom |
| Date: | 2015–06–18 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureir:78348&r=all |
| By: | Wang, X.; Agatz, N.A.H.; Erera, A. |
| Abstract: | Dynamic ride-sharing systems enable people to share rides and increase the efficiency of urban transportation by connecting riders and drivers on short notice. Automated systems that establish ride-share matches with minimal input from participants provide the most convenience and the most potential for system-wide performance improvement, such as reduction in total vehicle-miles traveled. Indeed, such systems may be designed to match riders and drivers to maximize system performance improvement. However, system-optimal matches may not provide the maximum benefit to each individual participant. In this paper we consider a notion of stability for ride-share matches and present several mathematical programming methods to establish stable or nearly-stable matches, where we note that ride-share matching optimization is performed over time with incomplete information. Our numerical experiments using travel demand data for the metropolitan Atlanta region show that we can significantly increase the stability of ride-share matching solutions at the cost of only a small degradation in system-wide performance. |
| Keywords: | ride-sharing, carpooling, sustainable transport, stable matching |
| Date: | 2015–05–27 |
| URL: | http://d.repec.org/n?u=RePEc:ems:eureri:78193&r=all |
| By: | Kadam, Sangram V. (Harvard University); Kotowski, Maciej H. (Harvard University) |
| Abstract: | We examine a dynamic, multi-period, bilateral matching market, such as a labor market where workers are long-lived and production occurs over a period of time. We define and identify sufficient conditions for the existence of a dynamically stable matching. Our framework accommodates many forms of inter-temporal preference complementarities, including a taste for variety and a status-quo bias. Extensions of our model incorporating imperfect information and financial transfers are proposed. We relate our analysis to market unraveling and to common market design applications, including the medical residency match. |
| JEL: | C78 |
| Date: | 2015–06 |
| URL: | http://d.repec.org/n?u=RePEc:ecl:harjfk:rwp15-030&r=all |