A stochastic differential game of capitalism

We develop a stochastic differential game of capitalism to analyze the role of uncertainty. In the deterministic game, the firm’s rent is completely taxed away and the firm stops investing completely. In the stochastic game, the government does not tax the firm’s rent completely. The firm posts a positive rate of investment if the firm’s rent exceeds the labor’s income. Although the cooperative solution is indeterminate, cooperation is always Pareto optimal compared to the non-cooperative Markovian Nash equilibrium. For individual rationality, we apply a payoff distribution procedure based on Yeung and Petrosyan (2006) to derive a subgame-consistent solution.     

重复占优策略博弈在团队培训中的应用及启发——基于一个体验式训练项目的思考

博弈论是研究决策主体行为发生直接相互作用时的决策以及这种决策的均衡问题的一门科学。占优策略博弈是指存在始终优于对方反应的博弈,占优策略博弈可能存在合作解和非合作解。在对一个基于重复非合作占优策略博弈而设计的培训项目进行分析的基础上,探讨有限重复占优策略博弈的非合作解和合作解的差别,并借鉴这种差别对于团队管理的启发,在管理实践中充分考虑主体的充分理性和最大化偏好,以团队利益为前提,尊重个体合理利益,设计科学的激励约束制度,促成一个良性的竞争合作团队氛围。     

Buying cooperation in an asymmetric environmental differential game

We consider a two-player asymmetric differential game of pollution control. One player is non-vulnerable to pollution, or unwilling to consider damages when choosing her production policy in a non-cooperative game. We characterize the feedback-Nash equilibrium and the cooperative solution. We establish conditions under which the vulnerable player can buy the cooperation of the non-vulnerable player to control her emissions. We further use the Nash bargaining solution to allocate the total cooperative dividend between the two players and propose a time-consistent decomposition overtime of the total payoff.     

Learning games

This paper presents a model of learning about a game. Players initially have little knowledge about the game. Through playing the same game repeatedly, each player not only learns which action to choose but also constructs a personal view of the game. The model is studied using a hybrid payoff matrix of the prisoner's dilemma and coordination games. Results of computer simulations show that (1) when all the players are slow at learning the game, they have only a partial understanding of the game, but might enjoy higher payoffs than in cases with full or no understanding of the game; (2) when one player is quick in learning the game, that player obtains a higher payoff than the others. However, all can receive lower payoffs than in the case in which all players are slow learners.     

Bargaining with independence of higher or irrelevant claims

This paper studies independence of higher claims and independence of irrelevant claims on the domain of bargaining problems with claims. Independence of higher claims requires that the payoff of an agent does not depend on the higher claim of another agent. Independence of irrelevant claims states that the payoffs should not change when the claims decrease but remain higher than the payoffs. Interestingly, in conjunction with standard axioms from bargaining theory, these properties characterize a new constrained Nash solution, a constrained Kalai–Smorodinsky solution, and a constrained Kalai solution.     

Weakly rational expectations

Aumann and Drèze (2008) characterised the set of interim expected payoffs that players may have in rational belief systems, in which there is common knowledge of rationality and a common prior. We show here that common knowledge of rationality is not needed: when rationality is satisfied in the support of an action-consistent distribution (a concept introduced by Barelli (2009)), one obtains exactly the same set of rational expectations, despite the fact that in such ‘weakly rational belief systems’ there may not be mutual knowledge of rationality, let alone common knowledge of rationality. In the special case of two-player zero-sum games, the only expected payoff is the minmax value, even under these weak assumptions.     

Can learning cause shorter delays in reaching agreements?

This paper uses a continuous-time war of attrition model to investigate how learning about private payoffs affects delays in reaching agreement. At each point in time, players may receive a private Poisson signal that completely reveals the concession payoff to be high (good-news learning) or low (bad-news learning). In the good-news model, the expected delay is always non-monotonic in the learning rate: an increase in the learning rate prolongs delay in agreement if the learning rate is sufficiently low. In the bad-news model, numerical examples suggest learning prolongs delay as well.     

Bayesian Nash equilibrium and variational inequalities

This paper provides a sufficient condition for the existence and uniqueness of a Bayesian Nash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobian matrix of the payoff gradient is negative definite for each state, then a Bayesian Nash equilibrium is unique. This result unifies and generalizes the uniqueness of an equilibrium in a complete information game by Rosen (1965) and that in a team by Radner (1962). In a Bayesian game played on a network, the Jacobian matrix of the payoff gradient coincides with the weighted adjacency matrix of the underlying graph.     

Rationality of bargaining solutions

The aim of this paper is to obtain the rationality of two-person bargaining solutions by imposing usual assumptions in cooperative bargaining theory. In particular, it is proved that the conjunction of Independence of Irrelevant Alternatives and either Pareto Continuity or Strong Monotonicity implies this rationality.     

Rationalizability in continuous games

Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating “never-best-reply” strategies terminates before or at the first uncountable ordinal, and this bound is tight. Also, we examine the connection between this process and common belief of rationality in the universal type space of Mertens and Zamir (1985).     

Group versus Individual Performance Pay in Relational Employment Contracts when Workers are Envious

I compare group to individual performance pay when workers are envious and performance is nonverifiable. Avoiding payoff inequity, the group reward scheme is optimal as long as the firm faces no credibility problem. The individual reward scheme may, however, become superior albeit introducing the prospect of unequal pay. This is due to two reasons: Group incentives are relatively low‐powered compared to individual incentives, requiring higher incentive pay and impeding credibility of the firm. Moreover, with individual rewards, the firm benefits from the incentive‐strengthening effect of envy, allowing for yet smaller overall incentive pay and further softening the credibility constraint. I also show that contracts combining both individual and group rewards are often optimal, depending on the firm's credibility problem. These contracts include joint and relative performance pay schemes.     

Measure preserving derivatives and the pricing kernel puzzle

Recent empirical studies have found evidence of nonmonotonicity in the pricing kernels for a variety of market indices. This phenomenon is known as the pricing kernel puzzle. The payoff distribution pricing model of Dybvig predicts that the payoff distribution of a direct investment of $1 in a market index may be replicated by investing less than $1 in some derivative written on that market index whenever the associated pricing kernel is nondecreasing. Using the Hardy–Littlewood rearrangement inequality, we obtain an explicit solution for the cheapest replicating derivative, which we refer to as the optimal measure preserving derivative. The optimal measure preserving derivative is the permutation appearing in Ryff’s decomposition of the pricing kernel with respect to the market payoff measure. We compute optimal measure preserving derivatives corresponding to the estimated physical and risk neutral distributions in the paper by Jackwerth (2000) that first brought attention to the pricing kernel puzzle.     

Evolutionary stability of altruism and envy in Tullock contests

This paper considers Tullock contests with altruistic and envious individuals as players. Altruism (envy) is beheld as another motivation for low (high) dissipation rates in contests. A pure population of altruists has higher payoffs than a purely envious population, but the altruist has a lower payoff if he is confronted with an envious individual. In an evolutionary approach in which the population share of the type with the higher material payoff rises, it can be shown that there is a possibility of either envy or altruism becoming extinct. Furthermore, we find an advantage of envy in such a manner that very altruistic individuals always die out, but very envious ones only do so under certain conditions. I am grateful to Alexander Haupt, two anonymous referees, and the editor for constructive comments on this paper.     

Null players,solidarity, and the egalitarian Shapley values

The Shapley value probably is the most eminent single-point solution concept for TU-games. In its standard characterization, the null player property indicates the absence of solidarity among the players. First, we replace the null player property by a new axiom that guarantees null players non-negative payoffs whenever the grand coalition’s worth is non-negative. Second, the equal treatment property is strengthened into desirability. This way, we obtain a new characterization of the class of egalitarian Shapley values, i.e., of convex combinations of the Shapley value and the equal division solution. Within this characterization, additivity and desirability can be replaced by strong differential monotonicity, which translates higher productivity differentials into higher payoff differentials.     

Are athletes more cooperative than nonathletes? A laboratory experiment

Former athletic employees receive a better wage when hired than other employees because recruiters associate positive values to athletic participation. Whereas athletes are considered as more cooperative than others, this assumption lacks empirical support. We implement a laboratory experiment in order to examine whether athletes (i.e., individuals engaged in intense athletic participation) exhibit more cooperative behaviours than nonathletes. We compare the cooperative behaviours of athletes and nonathletes in a single‐shot public good game using a variant of the strategy method. We find that athletes exhibit significantly more conditional cooperative behaviours than nonathletes but no significant differences in unconditional behaviours.     

Rationality in supplier selection decisions: The effect of the buyer's national task environment

Our study sheds light on two fundamental questions in supply management: First, does adherence to highly rational decision processes help buyers make better supplier selection decisions? Second, is the influence of procedural rationality on decision effectiveness moderated by buyers’ (differently dynamic) task environments? We empirically test these questions using a sample of 150 supplier selection decisions taken in China and 150 decisions taken in Germany, countries that expose buyers to dynamic decision environments and stable decision environments, respectively. Our findings suggest that the influence of decision process rationality is stable across decision makers’ task environments. Both in China and in Germany, such process rationality is positively related with higher decision quality, and no significant differences in relationship strengths emerge between the two country samples.     

Sovereign default risk,debt uncertainty and fiscal credibility: The case of Brazil

Since Credit Default Swaps spreads reflect the sovereign risk and, thus, the uncertainties related to government solvency, the goal of this study is to examine the relation between sovereign risk and debt uncertainty (measured by the disagreement in expectations about public debt) in an important developing country – Brazil. Furthermore, the paper analyzes whether fiscal credibility plays a key role in mitigating the effect of debt uncertainty on sovereign risk. The results suggest the disagreement in expectations about public debt affects the sovereign risk, and fiscal credibility plays a twofold role, it reduces sovereign risk, and it mitigates the effect of debt uncertainty on sovereign risk. Besides, quantile regression estimates reveal that fiscal credibility improvements are even more important when sovereign risk levels are higher.     

Dynamic coordination among heterogeneous agents

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 a set of beliefs that would make this coincidence possible exists. However, the equilibrium thresholds 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. In the efficient solution, agents follow others even more often.     

Deterministic multi-player Dynkin games

A multi-player Dynkin game is a sequential game in which at every stage one of the players is chosen, and that player can decide whether to continue the game or to stop it, in which case all players receive some terminal payoff.We study a variant of this model, where the order by which players are chosen is deterministic, and the probability that the game terminates once the chosen player decides to stop may be strictly less than 1.We prove that a subgame-perfect ε-equilibrium in Markovian strategies exists. If the game is not degenerate this ε-equilibrium is actually in pure strategies.     

Overinvestment in partially relationship-specific assets and R&D

This paper considers a firm that can engage in partially relationship specific investments. The firm does not have the option to engage in investments that are not at all relationship specific. I show that, in such a setting, equilibrium investment may exceed the socially optimal level. This is contrary to the intuition obtained from standard idiosyncratic (i.e., relationship-specific) investment models, in which the possibility of “hold-up” leads to underinvestment. The driving force behind this result is that when assets are only partially relationship-specific, marginal investment may yield higher benefits when transacting with the market at large even though cumulative investment yields higher benefits within a bilateral relationship. This finding is relevant to many bilateral relationships in which investments that are targeted to improve the joint payoff of the relationship inevitably have spillover effects that improve the payoff of transacting with the market.