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。     

Piecewise closed-loop equilibria in differential games with regime switching strategies

We propose a new methodology exploring piecewise closed-loop equilibrium strategies in differential games with regime switching actions. We develop a general game with two players. Players choose an action that influences the evolution of a state variable, and decide on the switching time from one regime to another. Compared to the optimal control problem with regime switching, necessary optimality conditions are modified for the first player to switch. When choosing her optimal switching strategy, this player considers the impact of her choice on the other player’s actions and consequently on her own payoffs. In order to determine the equilibrium timing of regime changes, we derive conditions that help eliminate candidate equilibrium strategies that do not survive deviations in switching strategies. We then apply this new methodology to an exhaustible resource extraction game.     

Time consistent side payments in a dynamic game of downstream pollution

This note determines a rule to share a surplus gained when two countries or regions agree to coordinate their policies to reduce downstream pollution. An intertemporal decomposition scheme for the total side payment is proposed. This scheme has the following individual rationality property: in each subgame that starts along the cooperative trajectory, one country is guaranteed to receive a higher payoff in the cooperative solution than in the disagreement solution. For this country another notion of individual rationality obtains: this country will at any instant of time during the play of the game receive a higher payoff in the cooperative solution than in the disagreement solution.     

Sad-Loser contests

We consider asymmetric winner-reimbursed contests. It turns out that such contests (Sad-Loser) have multiple internal pure-strategy equilibria (where at least two players are active). We describe all equilibria and discuss their properties. In particular, we find (1) that an active player is indifferent among all her non-negative choices and her expected payoff is zero in any internal equilibrium, (2) that a higher-value (stronger) player always spends less than a lower-value (weaker) player and therefore always has a lower chance to win a Sad-Loser contest in any internal equilibrium, and (3) a sufficient condition for a net total spending to be higher in a Sad-Loser contest than in the corresponding asymmetric contest.     

Voting, bargaining, and factor income distribution

The effect of possible price control on factor income distribution under a democratic system is examined in the context of a collective bargaining model. A solution concept of the cooperative game theory called the Harsanyi-Shapley value is chosen to predict a likely outcome. The explicit solution for a non-atomic production economy, with two production factors and a fixed coefficient technology, is obtained. We find that this solution can be realized through prices. It is observed that in this solution, factor income shares respond to the ratio of the total endowments of two factors.     

Debt contracts and cooperative improvements

In this paper, we consider a dynamic game with imperfect information between a borrower and lender who must write a contract to produce a consumption good. In order to analyze the game, we introduce the concept of a coalitional perfect Bayesian Nash equilibrium (cPBNE). We prove that equilibria exist and are efficient in a precise sense, and that deterministic contracts that resemble debt are optimal for a general class of economies. The cPBNE solution concept captures both the non-cooperative aspect of firm liquidation and the cooperative aspect of renegotiation.     

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.     

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.     

Mechanism design for a solution to the tragedy of commons

We consider the problem of the tragedy of commons in cooperative production economies, and propose a mechanism to resolve this tragedy, taking into account that the coordinator cannot perfectly monitor each agent’s labor skill and each agent may have an incentive to overstate as well as understate his own skill. Even in such a situation, the mechanism implements the proportional solution (Roemer in Soc Philos Policy 6:74–92, 1989 and Roemer and Silvestre in J Econ Theory 59:426–444, 1993) in Nash and strong equilibria when it is played as a normal form game. Moreover, the mechanism triply implements the solution in Nash, subgame-perfect, and strong equilibria when it is played as a two-stage extensive form game. We are greatly thankful to Semi Koray, William Thomson, and an anonymous referee of this journal for their concrete and helpful comments on improving the paper. An earlier version of this paper was presented at the annual meeting of the Japanese Economic Association held at Hitotsubashi University in October 2001 and at the Conference on Economic Design held at NYU in July 2002. We are grateful to Takehiko Yamato for his useful comments in the former conference. We are also thankful to Tatsuyoshi Saijo, Kotaro Suzumura, and Yoshikatsu Tatamitani for their kind comments.     

Majority rule with dollar voting

Consider a majority game in which each player's voting strength is equal to the player's payoff. In this game, wealth is the only source of power, and any coalition with more than half the wealth can take everything. Only extreme concentrations of wealth, in which one player owns everything or two players each own half the total wealth are undominated, and thus constitute the core. However, the stable set (von Neumann-Morgenstern solution) is significantly larger. Allocations in which one player has half the wealth, or which divide the total wealth equally among a number of players equal to a power of two, constitute the unique stable set. The stable set thus provides a formal model of an endogenous balance of power.     

Cost-sharing in directed networks: Experimental study of equilibrium choice and system dynamics

This study reports the results of an experiment on directed networks with positive externalities induced by cost-sharing. Subjects participated in a network game in which they had to choose between private and public transportations. If a player chose public transportation, then she shared the travel cost equally with other players making the same choice, whereas if she chose private transportation, then her travel cost was fixed. Travel costs on the private route were manipulated across the two experimental conditions. In one condition, these costs were homogeneous among players; in the other condition, they were heterogeneous among players and only privately known. We found that half (none) of the player groups in the homogeneous (heterogeneous) condition converged toward the efficient equilibrium. Examination of the system dynamics shows that convergence toward efficiency was facilitated by: (1) the existence of an intermediate equilibrium choice; and (2) strategic teaching by which a farsighted player chooses strategies with poor short-term payoff in order to shift group decisions to the efficient equilibrium and thereby increase her own long-term benefit.     

Deadlines in stochastic contests

We consider a two-player contest model in which breakthroughs arrive according to privately observed Poisson processes. Each player’s process continues as long as she exerts costly effort. The player who collects the most breakthroughs until a predetermined deadline wins a prize.We derive Nash equilibria of the game depending on the deadline. For short deadlines, there is a unique equilibrium in which players use identical cutoff strategies, i.e., they continue until they have a certain number of successes. If the deadline is long enough, the symmetric equilibrium distribution of an all-pay auction is an equilibrium distribution over successes in the contest. Expected efforts may be maximal for a short or intermediate deadline.     

Categorization and correlation in a random-matching game

We consider a random-matching model in which every agent has a categorization (partition) of his potential opponents. In equilibrium, the strategy of each player i is a best response to the distribution of strategies of his opponents (when they face i) in each category of his categorization. We provide equivalence theorems between distributions generated by equilibrium profiles and correlated equilibria of the underlying game.     

网络游戏品质对玩家忠诚度的影响——沉浸体验的中介效应

中国网络游戏市场保持高速增长的势态，吸引了大量的竞争者进入这个行业。面对竞争，如何吸引玩家、保持玩家忠诚度己经成为网络游戏运营商最关心的问题。本文在回顾相关文献的基础上提出了研究假设，并通过网络调查方法收集数据，最后，通过回归分析验证假设，研究发现：网络游戏品质对玩家忠诚度有直接影响，同时有部分影响效应是通过沉浸体验间接实现的；在网络游戏品质、沉浸体验、运营商的可信度三者中，沉浸体验对网络游戏忠诚度的影响效应最大。     

Characterization of the Average Tree solution and its kernel

In this article, we study cooperative games with limited cooperation possibilities, represented by a tree on the set of agents. Agents in the game can cooperate if they are connected in the tree. We first derive direct-sum decompositions of the space of TU-games on a fixed tree, and two new basis for these spaces of TU-games. We then focus our attention on the Average (rooted)-Tree solution (see Herings et al. (2008)). We provide a basis for its kernel and a new axiomatic characterization by using the classical axiom for inessential games, and two new axioms of invariance called Invariance with respect to irrelevant coalitions and Weighted addition invariance on bi-partitions. We also solve the inverse problem for the Average (rooted)-Tree solution.     

矩阵对策中混合对策问题的数学模型及lingo求解

对策论是研究对抗问题的理论与方法。矩阵对策是最常见,也是最重要的对策。通过对矩阵对策中混合对策问题的分析,建立了局中人最优策略的线性规划模型,并给出了模型的lingo求解方法。     

Weakly balanced contributions and the weighted Shapley values

We provide a concise characterization of the class of positively weighted Shapley values by three properties, two standard properties, efficiency and marginality, and a relaxation of the balanced contributions property called the weak balanced contributions property. Balanced contributions: the amount one player gains or loses when another player leaves the game equals the amount the latter player gains or loses when the former player leaves the game. Weakly balanced contributions: the direction (sign) of the change of one player’s payoff when another player leaves the game equals the direction (sign) of the change of the latter player’s payoff when the former player leaves the game. Given this characterization, the symmetric Shapley value can be “extracted”from the class of positively weighted Shapley values by either replacing the weak balanced contributions property with the standard symmetry property or by strengthening the former into the balanced contributions property.     

COALITION FORMATION AND BARGAINING PROTOCOLS: A REVIEW OF THE LITERATURE

This paper offers a review of the vast literature regarding bargaining and coalition formation. This topic has been generally described as the attempt to provide strategic foundations to cooperative solution concepts. It can therefore be seen as the linking ring between the non‐cooperative and the cooperative game‐theoretic approach to coalition formation. Its central role in economic theory and its relatively long history that goes back to the Nash program have fostered a large academic production, including surveys. Nonetheless, this paper will focus on an aspect that is often neglected in the dedicated surveys: the specificities of the bargaining protocols leading to different outcomes. Although generally downgraded to the rank of details, the differences in bargaining protocols, even when minor, can cause significant changes in fundamental aspects such as the possibility to reach full cooperation, the distribution of final pay‐offs and the time taken to reach an agreement. Focused on externalities‐free games, therefore on bargaining protocols sustaining solution concepts for cooperative games in characteristic function form, the paper aims at providing a brief but exhaustive review of the topic that could result in a very useful tool for any researcher approaching the subject of coalitional bargaining.     

Gradient dynamics in population games: Some basic results

When each player in a population game continuously adjusts her action to move up the payoff gradient, then the state variable (the action distribution) obeys a nonlinear partial differential equation. We find conditions that render gradient adjustment myopically optimal and analyze two broad classes of population games. For one class, we use known results to establish the existence and uniqueness of solutions to the PDE. In some cases, these solutions exhibit shock waves or rarefaction waves. For a second class, we use a local form of Nash equilibrium to characterize the steady state solutions of the PDE and find sufficient conditions for asymptotic convergence.     

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.