Cheng-Zhong Qin

Endogenous transfers in the Prisoner's Dilemma game: An experimental test of cooperation and coordination

We study experimentally a two-stage compensation mechanism for promoting cooperation in prisoners dilemma games. In stage 1, players simultaneously choose binding non-negative amounts to pay their counterparts for cooperating in a given prisoners dilemma game, and then play the prisoners dilemma game in stage 2 with knowledge of these amounts. For the asymmetric prisoners dilemma games we consider, all payment pairs consistent with mutual cooperation in subgame-perfect equilibrium transform these prisoners dilemma games into coordination games, with both mutual cooperation and mutual defection as Nash equilibria in the stage-2 game. We find considerable empirical support for the mechanism, as cooperation is much more common when these endogenous transfer payments are feasible. We identify patterns among transfer pairs that affect the likelihood of cooperation. Mutual cooperation is most likely when the payments are identical; it is also substantially more likely with payment pairs that bring the payoffs from mutual cooperation closer together than with payment pairs that cause them to diverge. We also find that transfers are effective in sustaining cooperation even when they are imposed and not chosen.

Equilibrium Prices when the Sunspot Variable is Continuous

We analyze sunspot-equilibrium prices in nonconvex economies with perfect markets and a continuous sunspot variable. Our primary result is that every sunspot equilibrium allocation can be supported by prices that, when adjusted for probabilities, are constant across states. This result extends to the case of a finite number of equally probable states under weak nonsatiation conditions, but does not extend to general discrete state spaces. We use our primary result to establish the equivalence of the set of sunspot equilibrium allocations based on a continuous sunspot variable and the set of lottery equilibrium allocations

A conjecture of Shapley and Shubik on competitive outcomes in the cores of NTU market games

It is shown that for every NTUmarket game, there is amarket thatrepresents the game whosecompetitive payoff vectors completely fill up theinner core of the game. It is also shown that for every NTU market game and for any point in its inner core, there is a market that represents the game and further has the given inner core point as itsunique competitive payoff vector. These results prove a conjecture of Shapley and Shubik.Journal of Economic Literature Classification Numbers: C71, D51.

On Market Games When Agents Cannot Be in Two Places at Once

Abstract We consider markets in which agents supply their time or the services of a capital good and the duration of the market is limited. We show that a coalitional game can be generated by such a market if and only if the characteristic function of the game is superadditive. Journal of Economic Literature Classification Numbers: C71, D51.

Fashion and Homophily

We analyze a model of evolution of fashion based on a social network game, to be referred to as a fashion game. Each agent in this model is either a conformist or a rebel. A conformist prefers to take the action that is most common among her neighboring agents, whereas a rebel prefers the opposite. When there is only one type of agents, the fashion game possesses an exact potential function and, thus, fashion cycles are unlikely to emerge. This confirms the insightful observation of Simmel (1904) that the heterogeneity of consumers is essential to the emergence of fashion cycles. However, the population composition is not so important. What matters is a more subtle structure factor called the homophily index. Our main finding is that a higher homophily index generally inhibits the emergence of fashion cycles. This is established through the potential analysis, the partial potential analysis, and the stability analysis of a system of ordinary differential equations that is transformed from the stochastic best response dynamic of the fashion game by applying mean-field approximations and the diffusion approximation. In particular, the partial potential analysis is introduced in this paper as an extension of the seminal potential analysis.

An Inner Core Equivalence Theorem

SummaryWe extend the notion of the inner core of a finite economy to a large economy. We prove that competitive allocations and the core coincide with the inner core.

Shapley's Conjecture on the Cores of Abstract Market Games

Shapley (1955) introduced the model of an abstract market game as a generalization of the assignment game model, among several other models. He conjectured that abstract market games possess non-empty cores. We analyze properties of abstract market games and provide a proof of this conjecture for cases with four or fewer players. We show by example that, in general, the structure of an abstract market game is not strong enough to guarantee the nonemptiness of the core. We establish supplemental conditions for the conjecture to hold. Our supplemental conditions are satisfied by the assignment games and abstract market games with one side consisting of a single player as with package auction games in Ausubel and Milgrom (2002).

Dynamic Matching Pennies on Networks

We consider a network game based on matching pennies with two types of agents, conformists and rebels. Conformists prefer to match the action taken by the majority of her neighbors while rebels like to match the minority. We investigate the simultaneous best response dynamic focusing on the lengths of limit cycles (LLC for short). Our results imply that the network structure generally plays a very crucial role in determining LLC. When the network is a line or a ring, for almost all type configurations, LLC=1, meaning that a pure strategy Nash equilibrium is reached, regardless of the initial action profiles. However, when the network is a star, LLC=4 for approximately half of the type configurations. The ordinal potential property and the sequential best response dynamic are also studied.Fashion, as a “second nature” of human being, has great economic impacts. In this paper, we apply a heterogenous network game to analyze the existence of a fashion cycle. There are two types of agents in the network game, conformists and rebels. Conformists prefer to match the action taken by the majority of her neighbors while rebels like to mismatch. Our results imply that social interaction structures play a crucial role in the evolution of fashion, especially the emergence of fashion cycles. For example, with a social network composed of a line or a ring, fashion will almost always evolve into a steady state where no flux is possible and thus can be deemed as disappeared. When the network is a star, however, for approximately half of all the configurations of agents’ types, a fashion cycle of length 4 will always emerge, regardless of the initial action profiles. ∗This is a sister working paper with: Bo-yu Zhang, Zhi-gang Cao, Cheng-zhong Qin, Xiao-guang Yang, Fashion and Homophily (April 14, 2013). Available at SSRN: http://ssrn.com/abstract=2250898 or http://dx.doi.org/10.2139/ssrn.2250898. The research of the first and third authors are supported by the 973 Program (2010CB731405) and National Natural Science Foundation of China (71101140). We gratefully acknowledge helpful discussions with Xujin Chen, Zhiwei Cui, Xiaodong Hu, Weidong Ma, Changjun Wang, Lin Zhao, and Wei Zhu. †Key Laboratory of Management, Decision & Information Systems, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. Email: zhigangcao@amss.ac.cn. ‡Department of Economics, University of California, Santa Barbara, CA 93106, USA. Email: qin@econ.ucsb.edu. §Key Laboratory of Management, Decision & Information Systems, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. Email: xgyang@iss.ac.cn. ¶Department of Mathematics, Beijing Normal University, Beijing, 100875, China. Email: zhangboyu5507@gmail.com.

Finite-order type spaces and applications

We propose a framework of consistent finite-order priors to facilitate the incorporation of higher-order uncertainties into Bayesian game analysis, without invoking the concept of a universal type space. Several recent models, which give rise to stunning results with higher-order uncertainties, turn out to operate with certain consistent order-2 priors. We introduce canonical representations of consistent finite-order priors, which we apply to establish a criterion for determining the orders of strategically relevant beliefs for abstract Harsanyi type spaces. We derive finite-order projections of type spaces and discuss convergence of BNEs based on them as the projection order increases. Finally, we introduce finite-order total variation distances between priors, which are suitable for analyzing the issues on equilibrium continuity and robustness. We revisit recent advancements of Bayesian game theory and develop new insights based on our framework.

Concavifiability and the marginal rate of substitution

Abstract We provide a condition for testing non-concavifiability of preference relations that utilizes the marginal rate of substitution. The result is derived from Kannais Proposition 2.1 (ii) in Journal of Mathematical Economics 4, 1977, pp. 1-56.