基于系统动力学的地方政府与制造企业碳减排演化博弈分析

为探究中国在碳减排政策下地方政府与制造企业双方的博弈关系,在分析地方政府和制造企业不同策略下的成本和收益的基础上,采用系统动力学方法构建了地方政府和制造企业之间的静态混合策略演化博弈模型;进一步引入政府动态惩罚和补偿策略,剖析政企双方策略的互动机制。分析结果表明:地方政府对企业是否采取碳减排措施的奖惩力度、企业采取碳减排措施的成本与收益,会直接影响博弈结果;地方政府和制造企业两个群体在三种情况下存在演化稳定策略;在一定条件下,系统演化呈现周期性特征;当地方政府实施动态惩罚或补偿措施时,该博弈模型存在稳定的Nash均衡点。     

Strategic bidding in continuous electricity auctions: an application to the Spanish electricity market

In this paper we introduce an asymmetric model of continuous electricity auctions with limited production capacity and bounded supply functions. The strategic bidding is studied with this model by means of an electricity market game. We prove that for every electricity market game with continuous cost functions a mixed-strategy Nash equilibrium always exists. In particular, we focus on the behavior of producers in the Spanish electricity market. We consider a very simple form for the Spanish electricity market: an oligopoly consisting just of independent hydro-electric power production units in a single wet period. We show that a pure-strategy Nash equilibrium for the Spanish electricity market game always exists.     

Convergence conditions for the Brown-Robinson iterative method for bimatrix games

The article considers the convergence of the Brown-Robinson iterative method to find a mixed-strategy equilibrium in a bimatrix game. The known result on convergence to an equilibrium for a zero-sum game is generalized to a wider class of games that are reducible to zero-sum games by a composition of various transformations: addition of a constant to any column of the first-player payoff matrix; addition of a constant to any row in the second-player payoff matrix; multiplication of the payoff matrix by a positive constant α>0. Translated from Prikladnaya Matematika i Informatika, No. 2, pp. 69–83, 1999.     

Games with randomly disturbed payoffs: A new rationale for mixed-strategy equilibrium points

Equilibrium points in mixed strategies seem to be unstable, because any player can deviate without penalty from his equilibrium strategy even if he expects all other players to stick to theirs. This paper proposes a model under which most mixed-strategy equilibrium points have full stability. It is argued that for any gameΓ the players' uncertainty about the other players' exact payoffs can be modeled as a disturbed gameΓ ^*, i.e., as a game with small random fluctuations in the payoffs. Any equilibrium point inΓ, whether it is in pure or in mixed strategies, can “almost always” be obtained as a limit of a pure-strategy equilibrium point in the corresponding disturbed gameΓ ^* when all disturbances go to zero. Accordingly, mixed-strategy equilibrium points are stable — even though the players may make no deliberate effort to use their pure strategies with the probability weights prescribed by their mixed equilibrium strategies — because the random fluctuations in their payoffs willmake them use their pure strategies approximately with the prescribed probabilities.     

基于系统动力学的政府和废旧电子产品处理商演化博弈分析

文章为探究政府管制在废旧电子产品处理商实施生态拆解的作用,运用系统动力学方法构建了废旧电子产品处理问题中政府和处理商之间的一个混合策略演化博弈模型,并对政府管制策略选择与处理商实施生态拆解策略选择的互动机制进行了分析。演化博弈和系统仿真结果表明:处理商实施生态拆解和非生态拆解的收益、政府管制的有效性以及处理商实施非生态拆解受到惩罚等都直接影响系统的演化结果;政府和处理商两群体在3种情形下存在演化稳定策略;在一定的条件下,系统演化呈现周期性特征。最后从政府管制的角度出发,动态策略的演化博弈模型存在演化稳定的均衡点。     

Analysis of a dual-sourcing service provision game with symmetric and asymmetric vendors

This paper models a service provision game between two vendors under symmetric and asymmetric cost structures, who compete in first-period service quality levels with each other, with the aim of winning the larger share of the buyer’s fixed reward in the second period. This game differs from the previous studies in that the buyer maintains dual sourcing over two periods and thus has different characteristics. We show that this service provision game has distinct mixed-strategy equilibria with the vendors under symmetric and asymmetric cost structures. We find that the larger the winner’s share in the second period, the higher the vendors’ first-period service quality levels. However, increasing the winner’s share in the second period does not necessarily benefit the vendor with the lower marginal cost, but surely hurts the equilibrium profit of the vendor with the higher marginal cost.     

Monotonicity of the mapping associated with a noncooperative multiperson game

A noncooperative multiperson game can be associated with a mapping that generates a variational inequality. The problem of searching for Nash points in the game is equivalent to solving this inequality. Numerical methods for solving the variational inequality rely heavily on the monotonicity of the mapping generating the inequality. At the same time, the mapping associated with the noncooperative multiperson game may not be monotone. Necessary and sufficient conditions are established under which the mapping associated with a finite noncooperative mixed-strategy game of three or more persons is monotone.     

Implementability of correlated and communication equilibrium outcomes in incomplete information games

In a correlated equilibrium, the players’ choice of actions is directed by correlated random messages received from an outside source, or mechanism. These messages allow for more equilibrium outcomes than without any messages (pure-strategy equilibrium) or with statistically independent ones (mixed-strategy equilibrium). In an incomplete information game, the messages may also reflect the types of the players, either because they are affected by extraneous factors that also affect the types (correlated equilibrium) or because the players themselves report their types to the mechanism (communication equilibrium). Mechanisms may be further differentiated by the connections between the messages that the players receive and their own and the other players’ types, by whether the messages are statistically dependent or independent, and by whether they are random or deterministic. Consequently, whereas for complete information games there are only three classes of equilibrium outcomes, with incomplete information the corresponding number is 14 or 15 for correlated equilibria and even larger—15, 16 or 17—for communication equilibria. For both solution concepts, the implication relations between the different kinds of equilibria form a two-dimensional lattice, which is considerably more intricate than the single-dimensional one of the complete information case.     

造船企业与供应商产品质量演化博弈分析

船舶作为大型复杂系统产品,其上游供应商所提供的零部件质量会对最终产品的质量产生重要影响。在考虑造船企业和供应商质量策略和收益的基础上,本文构建了双方的演化博弈模型,对其策略的稳定性开展分析;进一步地,引入了造船企业的动态惩罚措施研究如何对双方的策略产生影响。研究结果表明:(1)造船企业对配套供应商采取产品质量提升措施的奖励和惩罚力度、供应商采取相应措施的收益与成本会直接影响博弈的相关结果;(2)造船企业和配套供应商在三种条件下存在各自的演化稳定策略,同时在一定条件下系统的演化过程呈现周期性质的特征;(3)当造船企业采取动态惩罚措施时,此博弈模型存在稳定的Nash均衡点。研究结果可以为造船企业督促供应商改善供货质量提供决策支持。     

Capacity and entry issues in online exchanges

With the advent of open standards and Internet technologies, the number of sellers who can participate in online exchanges is greatly increased. We model the competition between identical sellers vying for the same business, and find that there exists a mixed-strategy equilibrium in prices. The results help us understand the dynamics between a seller’s capacity and his motivation to participate in an auction.     

On an N-person noncooperative Markov game with a metric state space

We consider a noncooperative N-person discounted Markov game with a metric state space, and define the total expected discounted gain. Under some conditions imposed on the objects in the game system, we prove that our game system has an equilibrium point and each player has his equilibrium strategy. Moreover in the case of a nondiscounted game, the total expected gain up to a finite time can be obtained, and we define the long-run expected average gain. Thus if we impose a further assumption for the objects besides the conditions in the case of the discounted game, then it is proved that the equilibrium point exists in the nondiscounted Markov game. The technique for proving the nondiscounted case is essentially to modify the objects of the game so that they become objects of a modified Markov game with a discounted factor which has an equilibrium point in addition to the equilibrium point of the discounted game.     

Monotonicity in asymmetric first-price auctions with affiliation

I study monotonicity of equilibrium strategies in first-price auctions with asymmetric bidders, risk aversion, affiliated types, and interdependent values. Every mixed-strategy equilibrium is shown to be outcome-equivalent to a monotone pure-strategy equilibrium under the “priority rule” for breaking ties. This provides a missing link to establish uniqueness in the “general symmetric model” of Milgrom and Weber (Econometrica 50:1089–1122, 1982). Non-monotone equilibria can exist under the “coin-flip rule” but they are distinguishable: all non-monotone equilibria have positive probability of ties whereas all monotone equilibria have zero probability of ties. This provides a justification for the standard empirical practice of restricting attention to monotone strategies. Hendricks et al. (2003) provide an overview of recent empirical work. For a survey of experimental work, see Kagel and Levin (2002).     

AnN-person noncooperative discounted vector-valued dynamic game with a metric space

AnN-person noncooperative discounted vector-valued game with a metric space is investigated. We define aD-convex equilibrium point and prove that aD-convex equilibrium point exists in this game system. A modified version of the original game system is formulated so that an equilibrium point of the modified version is aD-convex equilibrium point of the original game system. Under appropriate conditions, the converse holds in the sense that aD-convex equilibrium point is also an equilibrium point of the modified game system.     

Crowding games are sequentially solvable

A sequential-move version of a given normal-form game Γ is an extensive-form game of perfect information in which each player chooses his action after observing the actions of all players who precede him and the payoffs are determined according to the payoff functions in Γ. A normal-form game Γ is sequentially solvable if each of its sequential-move versions has a subgame-perfect equilibrium in pure strategies such that the players' actions on the equilibrium path constitute an equilibrium of Γ.  A crowding game is a normal-form game in which the players share a common set of actions and the payoff a particular player receives for choosing a particular action is a nonincreasing function of the total number of players choosing that action. It is shown that every crowding game is sequentially solvable. However, not every pure-strategy equilibrium of a crowding game can be obtained in the manner described above. A sufficient, but not necessary, condition for the existence of a sequential-move version of the game that yields a given equilibrium is that there is no other equilibrium that Pareto dominates it. Received July 1997/Final version May 1998     

基于训练和过滤的期望均衡及其实现路径

期望均衡是博弈局中人或局外人对于博弈均衡点的一致期望,强调互利共赢,它要求博弈群体的每个成员对期望均衡点有一个共同的预期.显然,基于纳什均衡的帕累托优化组合策略是一个比纳什均衡更有效的期望均衡.要实现期望均衡,可采用局中人参与的训练与学习使得群体的预期一致,也可采用第三方过滤器来达到期望目标.在期望均衡的概率分布下,个体行为的偏离不能比均衡态取得更多收益.否则,训练就是无效的,第三方过滤器就是不公平的.     

Two noncooperative games between a coalition and its surrounding in a class of n-person games with constant sum

A cooperative game engendered by a noncooperative n-person game (the master game) in which any subset of n players may form a coalition playing an antagonistic game against the residual players (the surrounding) that has a (Nash equilibrium) solution, is considered, along with another noncooperative game in which both a coalition and its surrounding try to maximize their gains that also possesses a Nash equilibrium solution. It is shown that if the master game is the one with constant sum, the sets of Nash equilibrium strategies in both above-mentioned noncooperative games (in which a coalition plays with (against) its surrounding) coincide.     

Strategic behavior of experienced subjects in a common pool resource game

This paper describes the results of an experiment applying the strategy method to analyze the behavior of subjects in an 8-player common pool resource (CPR) game. The CPR game consists of a constituent game played for 20 periods. The CPR game has a unique optimum and a unique subgame perfect equilibrium; the latter involves overinvestment in the appropriation from the CPR. Sixteen students, all experienced in game theory, were recruited to play the CPR game over the course of 6 weeks. In the first phase of the experiment, they played the CPR game on-line 3 times. In the second phase of the experiment, the tournament phase, they designed strategies which were then played against each other. At the aggregate level, subgame perfect equilibrium organizes the data fairly well. At the individual level, however, fewer than 5% of subjects play in accordance with the game equilibrium prediction. Received May 1994/Final version August 1996     

One-to-many non-cooperative matching games

We study a strategic model of wage negotiations between firms and workers. First, we define the stability of an allocation in an environment where firms can employ more than one worker. Secondly, we develop a one-to-many non-cooperative matching game, which is an extension of Kamecke’s one-to-one non-cooperative matching game. The main result shows the equivalence between the stable allocations and the outcomes of the subgame equilibria in the matching game: for any stable allocation in this game there is a subgame perfect equilibrium which induces the allocation on the equilibrium path, and every subgame perfect equilibrium induces a stable allocation on the equilibrium path. Furthermore, as for the existence of a stable allocation, we argue that a stable allocation, as with a subgame perfect equilibrium, does not always exist, but it exists under some conditions, using Kelso and Crawford’s modelling.     

A noncooperativen-person semi-Markov game with a separable metric state space

A noncooperativen-person semi-Markov game with a separable metric state space is studied in this paper. We define the equilibrium condition of the noncooperative game, and find a necessary and sufficient condition for which the equilibrium condition holds, and prove that in our game system there possesses an equilibrium point so that each player has his own stationary equilibrium strategy.Partly supported by NSC Taiwan, R.O.C.     

Monitoring cooperative equilibria in a stochastic differential game

This paper deals with a class of equilibria which are based on the use of memory strategies in the context of continuous-time stochastic differential games. In order to get interpretable results, we will focus the study on a stochastic differential game model of the exploitation of one species of fish by two competing fisheries. We explore the possibility of defining a so-called cooperative equilibrium, which will implement a fishing agreement. In order to obtain that equilibrium, one defines a monitoring variable and an associated retaliation scheme. Depending on the value of the monitoring variable, which provides some evidence of a deviation from the agreement, the probability increases that the mode of a game will change from a cooperative to a punitive one. Both the monitoring variable and the parameters of this jump process are design elements of the cooperative equilibrium. A cooperative equilibrium designed in this way is a solution concept for a switching diffusion game. We solve that game using the sufficient conditions for a feedback equilibrium which are given by a set of coupled HJB equations. A numerical analysis, approximating the solution of the HJB equations through an associated Markov game, enables us to show that there exist cooperative equilibria which dominate the classical feedback Nash equilibrium of the original diffusion game model.This research was supported by FNRS-Switzerland, NSERC-Canada, FCAR-Quebec.