Non-self-averaging of a two-person game with only positive spillover: a new formulation of Avatamsaka’s dilemma

In this game [Aruka in Avatamsaka game structure and experiment on the web. In: Aruka Y (ed) Evolutionary controversies in economics. Springer, Tokyo, pp 115–132, 2001], selfishness may not be determined even if an agent selfishly adopts the strategy of defection. Individual selfishness can only be realized if the other agent cooperates, therefore gain from defection can never be assured by defection alone. The sanction by defection as a reaction of the rival agent cannot necessarily reduce the selfishness of the rival. In this game, explicit direct reciprocity cannot be guaranteed. Now we introduce different spillovers or payoff matrices, so that each agent may then be faced with a different payoff matrix. A ball in the urn is interpreted as the number of cooperators, and the urn as a payoff matrix. We apply Ewens’ sampling formula to our urn process in this game theoretic environment. In this case, there is a similar result as in the classic case, because there is “self-averaging” for the variances of the number who cooperate. Applying Pitman’s sampling formula to the urn process, the invariance of the random partition vectors under the properties of exchangeability and size-biased permutation does not hold in general. Pitman’s sampling formula depends on the two-parameter Poisson–Dirichlet distribution whose special case is just Ewens’ formula. In the Ewens setting, only one probability α of a new entry matters. On the other hand, there is an additional probability θ of an unknown entry, as will be argued in the Pitman formula. More concretely, we will investigate the effects of different payoff sizes from playing a series of different games for newly emerging agents. As Aoki and Yoshikawa (Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics, Economics Discussion Papers 2007-49. . November 26, 2007) and Aoki (J Econ Interact Coord 3:1–3, 2008) dealt with a product innovation and a process innovation, they criticized Lucas’ representative method and the idea that players face micro shocks drawn from the same unchanged probability distribution. In the light of Aoki and Yoshikawa (Non-self-averaging in macroeconomic models: a criticism of modern micro-founded macroeconomics, Economics Discussion Papers 2007-49. . November 26, 2007), we show the same argument in our Avatamsaka game with different payoffs. In this setting, innovations occurring in urns may be regarded as increases of the number of cooperators in urns whose payoffs are different.     

Repeated two-person zero-sum games with unequal discounting and private monitoring

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.     

The shared reward dilemma on structured populations

In this paper we study the recently introduced “shared reward dilemma” (Cuesta et al. in J Theor Biol 251:253–263, 2008) in the presence of a structure governing the interactions among the population. The shared reward dilemma arises when the prisoner’s dilemma is supplemented with a second stage in which a fixed reward is equally distributed among all cooperators. We first extend our previous results on the equilibrium structure of this game to the case of a one-shot game taking place on a regular network. Subsequently, we consider an evolutionary version of the game on both lattices and random networks. We show that the evolutionary game on graphs exhibits important differences with the case of well-mixed populations. In particular, there exists an important parameter range in which the cooperation is boosted and a single cooperator can invade a population of defectors. We study the dependence of the cooperation levels on the neighborhood size, finding that on random networks the level of cooperation reached decreases as the neighborhood size increases. Moreover, square lattices favor cooperation more than random networks, and on them cooperation may be almost full for certain parameter regions even for large neighborhood sizes. Further, we show that the effect of the population structure is never detrimental for cooperation. We interpret our results in terms of weak versus strong temptation and discuss the nontrivial issues involved in trying to promote cooperation exogenously by means of such a reward mechanism.     

Evolutionary stability of prospect theory preferences

We demonstrate that in simple 2×2 games (cumulative) prospect theory preferences can be (semi-)evolutionarily stable, in particular, a population of players with prospect theory preferences is stable against more rational players, i.e. players with a smaller degree of probability weighting. We also show that in a typical game with infinitely many strategies, the “war of attrition”, probability weighting is (semi-)evolutionarily stable. Finally, we generalize to other notions of stability. Our results may help to explain why probability weighting is generally observed in humans, although it is not optimal in usual decision problems.     

The Price of Envy—An Experimental Investigation of Spiteful Behavior

When receiving less resources than a competitor, envy may be evoked that may result in spiteful behavior. This paper applies evolutionary theory to understand envy and its outcomes. A theoretical framework is developed that is based on the cause–effect relationships of unequal outcomes, envy, defection of cooperation, and welfare loss. To test this framework, an experiment with 136 participants is run. The results confirm that receiving less than another can indeed lead to experiences of envy and defection of future cooperation, producing a welfare loss of one‐sixth. Copyright © 2014 John Wiley & Sons, Ltd.     

Heterogeneity in the resistance to learning

In this paper we analyze the effect of heterogeneity in the recently introduced “resistance to learning” (Jiménez et al. in Eur Phys J B 71:273–280, 2009a). In the context of the spatial Continuous Prisoner’s Dilemma, the resistance to learning has become a key mechanism for the emergence and maintenance of cooperation in a wide range of cost regimes. We extend the model to the case in which different individuals may have different levels of resistance. From non-cooperative initial states, the existence of heterogeneity in the resistance affects the cooperative behavior of unconditional imitators. These unconditional imitators, i.e., fast learners or individuals without resistance can achieve due to their interactions with gradual learners significant levels of cooperation. Our results confirm in one of its form the impact of heterogeneity and its role as a fundamental mechanism in promoting the emergence of cooperation.     

Best response dynamics with level-n expectations in two-stage games

This paper analyzes behavior in repeatedly played two-stage games, where players choose actions in both stages according to best replies using level-n expectations about the opponent׳s actions in both stages. Level-n expectations are recursively defined in a way that a player holding level-n expectations correctly predicts the action of an opponent holding level-(n−1) expectations. A general conceptual framework to study such dynamics for two-stage games is developed and it is shown that, contrary to results for single-stage games, the fixed points of the dynamics depend on the level of the expectations. In particular, for level-0 expectation, fixed points correspond to a Nash equilibrium of a simultaneous move version of the game, whereas (under certain conditions) fixed points converge towards the subgame perfect equilibrium of the two-stage game if the level of expectations goes to infinity. The approach is illustrated using a two-stage duopoly game, where firms in the first stage invest in activities reducing their marginal costs and in the second stage engage in Cournot competition. Conditions for local stability of the fixed points are derived for different levels of expectations and it is shown that level-2 expectations are sufficient to move the fixed-point of the dynamics to a close neighborhood of the subgame perfect equilibrium. Furthermore, it is demonstrated that although firms benefit from unilateral increases in the level of expectations, an increase of n by all firms reduces all profits.     

Secretary problems with inspection costs as a game

A secretary problem without recall, with given rewards and inspection costs is considered as a game of an opponent against a statistician. Probability distributions on the set of arrangements of the arrivals and randomized stopping rules are the strategies for the two players. We give a condition under which minimax strategies may be obtained in a systematic way.     

Stopping with congestion and private payoffs

This paper analyses a two-player stopping game with multiarmed bandits in which each player chooses between learning about the quality of her private risky arm and competing for the use of a single shared safe arm. The qualities of the players’ risky arms are independent. A player whose risky arm produces a success no longer competes for the safe arm. We assume that a player observes her opponent’s actions but not his realised payoffs. She is therefore never certain whether her opponent is still competing for the safe arm. When the players’ prior probabilities of success are sufficiently close, there exists no pure strategy equilibrium, and we characterise the unique mixed strategy equilibrium. Otherwise, the unique equilibrium is in pure strategies. The amount of experimentation performed in equilibrium is inefficiently low but, for many priors, higher than if successes are publicly observed.     

There is no ‘I’ in team: Career concerns,risk‐taking incentives,and team outcomes

The National Basketball Association contracting rules provide plausibly exogenous variation in career concerns near contract end. We use this setting to study how individual career concerns affect risk‐taking behavior and can sabotage team performance. Using the frequency and duration of player injuries from 1991 to 2013 we measure individual risk‐taking behavior. We find that the average player's likelihood of missing a game due to injury falls by 0.06 percentage points (or over 100% relative to the mean injury rate) in the final 3 months of his contract, and when missing games due to injury is unavoidable, his recovery time drops by 22 days. However, “elite” players with virtually no career concerns actually miss more games due to injury. Finally, we find that elite players missing too many games and “average” players playing before healthy, combine to hurt team performance. For each additional player in the last 3 months on contract, the win probability for that team falls by over 2.6%.     

Pareto-undominated and socially-maximal equilibria in non-atomic games

This paper makes the observation that a finite Bayesian game with diffused and disparate private information can be conceived of as a large game with a non-atomic continuum of players. By using this observation as its methodological point of departure, it shows that (i) a Bayes–Nash equilibrium (BNE) exists in a finite Bayesian game with private information if and only if a Nash equilibrium exists in the induced large game, and (ii) both Pareto-undominated and socially-maximal BNE exist in finite Bayesian games with private information. In particular, it shows these results to be a direct consequence of results for a version of a large game re-modeled for situations where different players may have different action sets.     

From Partners to Players: Extending the HR Playing Field

HR professionals must always be “becoming” or constantly changing and adapting. For the last decade, many have argued the business partner role as a complement to traditional HR administrative work. We argue in this paper that HR professionals should move beyond partners to become players. HR professionals as players are “in the game, on the field, making a difference” through their HR work. In this article, we suggest that to become players, HR professionals must learn to coach, architect, build, facilitate, lead, and provide a conscience to business leaders. Specific knowledge and tools for each of these roles are described. © 2001 John Wiley & Sons, Inc.     

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.     

Determinacy of equilibrium in outcome game forms

We show the generic finiteness of the number of probability distributions on outcomes induced by Nash equilibria for two-person game forms such that either (i) one of the players has no more than two strategies or (ii) both of the players have three strategies, and (iii) for outcome game forms with three players, each with at most two strategies. Finally, we exhibit an example of a game form with three outcomes and three players for which the Nash equilibria of the associated game induce a continuum of payoffs for an open non-empty set of utility profiles.     

Marginal effects of public employment on unconditional distribution of wage income in China

This paper examines the marginal effects of an employment expansion in China’s public sector on the unconditional distribution of “wage income” using the unconditional quantile estimation suggested by Firpo et al. (2009). Empirical data from the China Health and Nutrition Survey is split into three sub-samples to eliminate the effects of the Asian financial crisis in 1997 and the subprime financial crisis in 2008 on our empirical results. To explore the marginal effects, the empirical unconditional distributions of wage income “before” and “after” an expansion of the public employment have been graphed and compared. It has been found that an expansion of China’s public employment reduces the dispersion of wage income and hence alleviates income inequality in China. Besides, an expansion of public employment makes the symmetrical unconditional distribution of wage income become leftward skewed. Given these findings, an expansion of the public employment caused by the strategy of “guojin mintui” could mitigate China’s income inequality.     

Learning strategic cooperative behavior in industrial symbiosis: A game‐theoretic approach integrated with agent‐based simulation

This paper investigates the negotiation phase of industrial symbiosis relationships, where companies exchanging wastes for inputs need to develop strategies on how to share the additional costs to operate the industrial symbiosis business. The business behavior is approached as a “coopetition” problem where companies need to cooperate to reduce waste discharge costs and traditional input purchase costs and dive into competition to pay a minimum share of additional costs (i.e., waste treatment, waste transportation, and transaction costs) of operating industrial symbiosis. A noncooperative game‐theoretical model for sharing the additional costs is proposed that highlights the two strategies that companies can adopt aimed at sharing costs: a fair strategy and an opportunistic strategy. Then, an agent‐based model is used to simulate the game iterated over time and investigate how the players can adapt their strategies according to their past experience. Simulation results show that players learn that playing the fair strategy is beneficial in the long period, despite in the short period they can gain more benefit by playing the opportunistic strategy. Findings of the paper are critically important to reduce the business and managerial barriers against the formation of industrial symbiosis networks and to stimulate innovative thinking of company managers to foster the development of the circular economy. The paper proposes theoretical, managerial, and policy implications, which are discussed in detail in a comparative manner between linear and circular economy.     

Cores of many-player games; nonemptiness and equal treatment

This paper provides sufficient conditions to ensure nonemptiness of approximate cores of many-player games and symmetry of approximate core payoffs (the equal treatment property). The conditions are: (a) essential superadditivity—an option open to a group of players is to partition into smaller groups and realize the worths of these groups and (b) small group effectiveness (SGE)—almost all gains to collective activities can be realized by cooperation only within members of some partition of players into relatively small groups. Another condition, small group negligibility (SGN), is introduced and shown to be equivalent to SGE. SGN dictates that small groups of players cannot have significant effects on average (i.e., per capita) payoffs of large populations; thus, SGN is a analogue, for games with a finite player set, of the condition built into models with a continuum of player that sets of measure zero can be ignored. SGE implies per capita boundedness (PCB), that the supremum of average or per capita payoffs is uniformly bounded above. Further characterization of SGE in terms of its relationship to PCB is provided. It is known that if SGE does not hold, then approximate cores of many-player games may be empty. Examples are developed to show that if SGE does not hold and if there are players of “scarce types” (in other works, players with scarce attributes) then even if there is only a finite number of types of players and approximate cores are non-empty, symmetry may be lost; moreover, even players of abundant types may be treated asymmetrically by the core.     

A dynamic autoregressive expectile for time-invariant portfolio protection strategies

“Constant proportion portfolio insurance” is a popular technique among portfolio insurance strategies: the risky part of a portfolio is reallocated with respect to market conditions, via a fixed parameter (the multiple), guaranteeing a predetermined floor. We propose here to use a conditional time-varying multiple as an alternative. We provide the main properties of the conditional multiples for some mainstream cases, including discrete-time rebalancing and an underlying risk asset driven by the Lévy process, while evaluating conditional and unconditional gap risks. Finally, we evaluate the use of a dynamic autoregressive expectile model for estimating the conditional multiple in such a context.     

Responders’ dissatisfaction may provoke fair offer

In this article, we attempt to explain the fair outcome of ultimatum game experiments using the evolutionary dynamics. The players of the game, the proposers and the responders, are randomly matched to play the game. When the responders face low offers from the proposers, their decisions are influenced by not only the monetary payoff but also their feelings. To quantify the responders?? feelings, a degree of dissatisfaction is introduced into the game. Asymmetrical replicator dynamics is used to study the evolution of the proportion of players with different strategies. The solutions of the differential equations exhibit complex outcomes mainly depending on the degree of dissatisfaction. It could also be inferred from our results that people can maintain their rights and interests well when they have a strong sense of unfairness.     

供应链企业博弈的利益分析

企业的经营行为是建立在理性博弈基础之上的。本文从企业理性出发,分析了供应链企业在从自身利益出发和从供应链整体利益出发时博弈的企业得益和供应链整体得益,分析了企业在非合作博弈情形下风险分担的失效;并说明供应链企业合作对改进供应链效率的重要性,以及分析了供应链企业合作的前提条件。