A Unifying Pair of Cournot-Nash Equilibrium Existence Results

For games with a measure space of players a tandem pair, consisting of a mixed and a pure Cournot-Nash equilibrium existence result, is presented. Their generality causes them to be completely mutually equivalent. This provides a unifying pair of Cournot-Nash existence results that goes considerably beyond the central result of E. J. Balder (1995, Int. J. Game Theory24, 79-94, Theorem 2.1). The versatility of this pair is demonstrated by the following new applications: (i) unification and generalization of the two equilibrium distribution existence results by K. P. Rath (1996, J. Math. Econ.26, 305-324) for anonymous games, (ii) generalization of the equilibrium existence result of T. Kim and N. C. Yannelis (1997, J. Econ. Theory77, 330-353) for Bayesian differential information games, (iii) inclusion of the Bayesian Nash equilibrium existence results of P. R. Milgrom and R. J. Weber (1985, Math. Oper. Res.10, 619-632) and E. J. Balder (1988, Math. Operations Res.13, 265-276) for games with private information in the sense of J. C. Harsanyi (1967, Manage. Sci.14, 159-182). Journal of Economic Literature Classification Number: C72.     

Reciprocity—an indirect evolutionary analysis

This paper investigates agents who face a stylized pecuniary ‘game of life’ comprising the ultimatum game and the dictator game. Utility may but need not be attached to equity and reciprocity, as formalized by Falk and Fischbacher (Games Econom Behav, 54(2): 293–315, 2006) but, critically, this social component of preferences cannot be conditioned on whether an ultimatum or a dictator game is played. Evolutionary fitness of agents is determined solely by material success. Under these conditions, a strong preference for reciprocity, but little interest in equity as such evolves. Possible exogenous constraints that link reciprocity and equity concerns imply long-run levels of both which depend on the relative frequency of ultimatum vs. dictator interaction in agents’ multi-game environment. Financial support from the German Academic Exchange Service (DAAD) is gratefully acknowledged.     

Markov Perfect Equilibrium: I. Observable Actions

We define Markov strategy and Markov perfect equilibrium (MPE) for games with observable actions. Informally, a Markov strategy depends only on payoff-relevant past events. More precisely, it is measurable with respect to the coarsest partition of histories for which, if all other players use measurable strategies, each player's decision-problem is also measurable. For many games, this definition is equivalent to a simple affine invariance condition. We also show that an MPE is generically robust: if payoffs of a generic game are perturbed, there exists an almost Markovian equilibrium in the perturbed game near the initial MPE. Journal of Economic Literature Classification Numbers: C72, C73.     

Credibility costs in the monetary integration game*

Euro candidates are expected to maintain the value of their currency within the fluctuation band of the new exchange rate mechanism for at least two years. This paper highlights some unpleasant macroeconomic effects that could occur during this interval. The problem is cast as a two‐stage sequential game between private agents and the government of the applicant country. The policy‐maker decides whether to devaluate the domestic currency or not at two distinct dates; it makes a last choice just before accession to the monetary union. Under an assumption of incomplete information of private agents about the government's priorities on inflation and economic activity, the game presents a hybrid perfect Bayesian equilibrium. In the pooling configuration, an initial policy of zero devaluation does not signal the final devaluation decision. As private agents cannot completely rule out the risk of a ‘last devaluation’, a premium adds to interest rates and entails a systematic output loss.     

Equity-settled share-based payments and their (strategic) use under asymmetric information

Share-based payments are of widespread use in today's economy. Consulting firms are increasingly accepting equity compensation for their services (particularly from startups) and many governments provide fiscal incentives to support this choice. Likewise, profit-sharing licensing is an on-trend business practice by innovative firms and patent holders when transferring their technology to interested adopters. This paper unveils strategic considerations according to which an agent/seller designs its optimal policy in regard to the equity share to request in exchange for its service, technology, or trademark. The model assumes a fringe of interested users/customers differentiated by both the support they need from the seller and the value of the underlying relationship; and also holding an informational disadvantage on their own type. Given the seller's cost configuration, equilibrium outcomes entail entering a profit-sharing relationship either with the high-type customers only or with all customers. Yet, in this case, equity-based payment claims are —for rent extraction purposes— common (i.e., not differentiated) across types.     

Evolutionary dynamics and backward induction

The backward induction (or subgame-perfect) equilibrium of a perfect information game is shown to be the unique evolutionarily stable outcome for dynamic models consisting of selection and mutation, when the mutation rate is low and the populations are large.     

p-Dominance and Equilibrium Selection under Perfect Foresight Dynamics

This paper studies equilibrium selection based on a class of perfect foresight dynamics and relates it to the notion of p-dominance. A continuum of rational players is repeatedly and randomly matched to play a symmetric n×n game. There are frictions: opportunities to revise actions follow independent Poisson processes. The dynamics has stationary states, each of which corresponds to a Nash equilibrium of the static game. A strict Nash equilibrium is linearly stable under the perfect foresight dynamics if, independent of the current action distribution, there exists a consistent belief that any player necessarily plays the Nash equilibrium action at every revision opportunity. It is shown that a strict Nash equilibrium is linearly stable under the perfect foresight dynamics with a small degree of friction if and only if it is the p-dominant equilibrium with p<1/2. It is also shown that if a strict Nash equilibrium is the p-dominant equilibrium with p<1/2, then it is uniquely absorbing (and globally accessible) for a small friction (but not vice versa). Set-valued stability concepts are introduced and their existence is shown. Journal of Economic Literature Classification Numbers: C72, C73.     

Remittances as a social status signaling device

Like all human beings, migrants may have a concern about their prestige or social status in the eyes of left-home family and friends. They can remit money in order to signal their economic success and increase their status. We show that if migrants’ income is private information, unsuccessful migrants might accept a worsening of their living conditions and send back home large amounts of remittances only in order to make residents believe that they are successful. In some cases, successful migrants can signal their true favorable economic situation by remitting an even larger amount. The game presents various equilibria that differ with respect to the proportion and nature of the migrants who sacrifice consumption opportunities to status revealing actions.     

Fairness, errors and the power of competition

In this paper, we investigate the effects of competition on bargained outcomes. We show that the neglect of either fairness concerns or decision errors will prevent a satisfactory understanding of how competition affects bargaining. We conducted experiments which demonstrate that introducing a small amount of competition to a bilateral ultimatum game – by adding just one competitor – induces large behavioral changes among responders and proposers, causing large changes in accepted offers. Models that assume that all people are self-interested and fully rational do not adequately explain these changes. We show that a model which combines heterogeneous fairness concerns with decision errors correctly predicts the comparative static effects of changes in competition. Moreover, the combined model is remarkably good at predicting the entire distribution of offers in many different competitive situations.     

Conditions for equivalence between sequentiality and subgame perfection

We characterize the class of finite extensive forms for which the sets of Subgame Perfect and Sequential equilibrium strategy profiles coincide for any possible payoff function. In addition, we identify the class of finite extensive forms for which the outcomes induced by these two solution concepts coincide. We thank Luis Corchón, Francesco De Sinopoli, Herbert Gintis, Sjaak Hurkens, Francisco Marhuenda, Eric Maskin and four anonymous referees for helpful comments. Carlos thanks the financial support of the Spanish MEC through its FPI Grant BES-2003-0822. Cristian thanks the grant Plan de Formación de Personal Investigador de la Comunidad de Madrid and the financial support from project No. SEJ2004-00968/ECON from the Spanish Ministry of Education and Science. The usual disclaimer applies.     

Decomposing trust and trustworthiness

What motivates people to trust and be trustworthy? Is trust solely “calculative,” based on the expectation of trustworthiness, and trustworthiness only reciprocity? Employing a within-subject design, we run investment and dictator game experiments in Russia, South Africa and the United States. Additionally, we measured risk preferences and expectations of return. Expectations of return account for most of the variance in trust, but unconditional kindness also matters. Variance in trustworthiness is mainly accounted for by unconditional kindness, while reciprocity plays a comparatively small role. There exists some heterogeneity in motivation but people behave surprisingly similarly in the three countries studied.     

Inefficiency and social exclusion in a coalition formation game: experimental evidence

This paper experimentally investigates the impact of reciprocal behavior in multilateral bargaining and coalition formation. Our results show that reciprocal fairness strongly affects the efficiency and equity of coalition formation. In a large majority of cases, inefficient and unfair coalitions are chosen when their coalition values are relatively high. Up to one third of the experimental population is excluded from bargaining and earns nothing. In monetary terms economically significant efficiency losses occur. We find that the interplay of selfish and reciprocal behavior unavoidably leads to this undesirable consequences. We also compare the predictions of recently developed models of social preferences with our experimental results. We find that some of these models capture the empirical regularities surprisingly well.     

On economic applications of evolutionary game theory

Evolutionary games have considerable unrealized potential for modeling substantive economic issues. They promise richer predictions than orthodox game models but often require more extensive specifications. This paper exposits the specification of evolutionary game models and classifies the possible asymptotic behavior for one and two dimensional models.     

Equilibrium in a Market Game

This paper studies the equilibrium of an exchange economy with the same number of agents and commodities. It is shown that under rather mild conditions on demand the market have a price equilibrium—independently of the divisibility of the commodities. The result extends Gale’s equilibrium theorem for indivisible commodities to the case where some commodities are perfectly divisible. The proof is based on a topological lemma contained in previous paper of one of the authors.     

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 a nonsatiation condition, 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. Journal of Economic Literature Classification Numbers: D51, D84, E32.     

管子轻重理论的均衡思想

<管子>后16篇,也称轻重篇,着重阐述了轻重理论,是中国古代特有的一种经济管理思想.前人学者大多从供求规律与货币数量论等角度对商品之间的轻重规律进行阐释.文章则重点阐述了轻重规律所蕴含的均衡思想,并且在阐述管子轻重理论中蕴含的局部均衡、动态均衡、一般均衡思想后,借用现代经济学的分析工具,试图重建管子轻重规律的均衡分析.西方经济学直到1769年以后才在经济学中引入均衡的概念,此研究将进一步丰富中国经济思想的研究.     

Equilibrium Dynamics in a Two-Sector Model with Taxes

In this paper we are concerned with the equilibrium dynamics of a two-sector model of endogenous growth with distortionary taxes. We show that for certain parameters values and tax schemes every equilibrium orbit—except the steady state solution—is non-interior; i.e., there are times in which one of the sectors is inactive. This analysis confirms that in multisector models the set of easily checkable, universal conditions that can guarantee the interiority of equilibrium solutions is rather limited. Journal of Economic Literature Classification Numbers: D90, E22.     

Walras and Darwin: an odd couple?

General equilibrium theory and the evolutionary branches of economics and game theory take rather opposite positions in the spectrum covered by the economic science. However, we reveal and explore analogies between Darwinian dynamics and Walrasian tatonnement processes for pure exchange economies, as well as further analogies implied by these.     

Equilibrium unemployment and retirement

We first propose some new empirical evidence on the fact that the labor market conditions matter for the retirement decision at the individual level: we investigate whether unemployed workers retire before employed workers, other things being equal. Our main objective in this paper is then to propose an equilibrium unemployment approach to retirement decisions that allows us to derive the positive and normative features of retirement decisions when search and matching frictions are considered. Two main conclusions emerge: the retirement decision of unemployed workers depends on the labor-market frictions whereas that of employed workers does not; the existence of search externalities makes the retirement age of unemployed workers intrinsically suboptimal. Considering Social Security policy issues, we show that the complete elimination of the implicit tax on continued activity is not necessarily welfare-optimizing in a second best world where the labor market equilibrium suffers from distortions.