Adjustment patterns and equilibrium selection in experimental signaling games

This paper examines the relation between adjustment patterns and equilibrium selection in laboratory experiments with two types of simple signaling games. One type of game has two Nash equilibria, of which only one is sequential. The other type has two sequential equilibria, only one of them satisfying equilibrium dominance. For each type of game, the results show that variations in the payoff structure, which do not change the equilibrium configuration, generate different adjustment patterns. As a consequence, the less refined equilibrium is more frequently observed for some payoff structures, while the more refined equilibrium is more frequently observed in others.     

Infrastructure security games

Infrastructure security against possible attacks involves making decisions under uncertainty. This paper presents game theoretic models of the interaction between an adversary and a first responder in order to study the problem of security within a transportation infrastructure. The risk measure used is based on the consequence of an attack in terms of the number of people affected or the occupancy level of a critical infrastructure, e.g. stations, trains, subway cars, escalators, bridges, etc. The objective of the adversary is to inflict the maximum damage to a transportation network by selecting a set of nodes to attack, while the first responder (emergency management center) allocates resources (emergency personnel or personnel-hours) to the sites of interest in an attempt to find the hidden adversary. This paper considers both static and dynamic, in which the first responder is mobile, games. The unique equilibrium strategy pair is given in closed form for the simple static game. For the dynamic game, the equilibrium for the first responder becomes the best patrol policy within the infrastructure. This model uses partially observable Markov decision processes (POMDPs) in which the payoff functions depend on an exogenous people flow, and thus, are time varying. A numerical example illustrating the algorithm is presented to evaluate an equilibrium strategy pair.     

两人进化博弈策略的决定机制与应用研究

通过建立一般情况下的两人进化博弈模型,给出了系统均衡点对应的矩阵行列式和迹表达式的经济含义,分析了16种典型情形下的进化稳定策略,详细讨论了均衡点稳定性分析结果所对应的博弈双方决策过程,从策略权衡的视角揭示了策略选择的内在机制。研究结果表明:不同策略前提下的相对净支付决定了系统的进化稳定策略,对方的策略选择以及自身可选策略的支付比较是影响博弈主体策略选择的两个基本要素,博弈主体会趋向于选择在对方策略既定下能够带来更大支付的策略。最后以环境治理中地方政府与企业以及地方政府之间的博弈关系为例,从对称博弈和非对称博弈两方面阐明了本文所构建模型在政策设计中的应用价值:针对不同案例,只要明确了两人博弈的支付矩阵,就可以通过计算相对净支付确定博弈双方的行为演化规律和稳定策略,从而简化计算过程,更加直接和更为便捷地为政策设计提供理论参考。     

Network capacity management under competition

We consider capacity management games between airlines who transport passengers over a joint airline network. Passengers are likely to purchase alternative tickets of the same class from competing airlines if they do not get tickets from their preferred airlines. We propose a Nash and a generalized Nash game model to address the competitive network revenue management problem. These two models are based on well-known deterministic linear programming and probabilistic nonlinear programming approximations for the non-competitive network capacity management problem. We prove the existence of a Nash equilibrium for both games and investigate the uniqueness of a Nash equilibrium for the Nash game. We provide some further uniqueness and comparative statics analysis when the network is reduced to a single-leg flight structure with two products. The comparative statics analysis reveals some useful insights on how Nash equilibrium booking limits change monotonically in the prices of products. Our numerical results indicate that airlines can generate higher and more stable revenues from a booking scheme that is based on the combination of the partitioned booking-limit policy and the generalized Nash game model. The results also show that this booking scheme is robust irrespective of which booking scheme the competitor takes.     

Timing of messages and the Aumann conjecture: a multiple-selves approach

The Aumann (In: Gabszewicz JJ, Richard JF, Wolsey L (eds) Economic decision making: games, econometrics and optimisation, 1990) conjecture states that cheap-talk messages do not necessarily help to coordinate on efficient Nash equilibria. In an experimental test of Aumann’s conjecture, Charness (Games Econ Behav 33(2):177–194, 2000) found that cheap-talk messages facilitate coordination when they precede the action, but not when they follow the action. Standard game-theoretical modeling abstracts from this timing effect, and therefore cannot account for it. To allow for a formal analysis of the timing effect, I study the sequential equilibria of the signaling game in which the sender is modeled as comprising two selves: an acting self and a signaling self. I interpret Aumann’s argument in this context to imply that all of the equilibria in this game are ‘babbling’ equilibria, in which the message conveys no information and does not affect the behavior of the receiver. Using this framework, I show that a fully communicative equilibrium exists—only if the message precedes the action but not when the message follows the action. In the latter case, no information is transmitted in any equilibrium. This result provides a game-theoretical explanation for the puzzling experimental results obtained by Charness (2000). I discuss other explanations for this timing-of-message effect and their relationship to the current analysis.     

直觉模糊多目标二人零和矩阵对策

研究矩阵对策是深入研究对策理论的一个基本途径和重要手段。根据直觉模糊多目标决策和模糊对策理论,研究了支付值为直觉模糊值的多目标二人零和矩阵对策。首先介绍了基于直觉模糊集的多目标二人零和矩阵对策模型,接着提出了求解直觉模糊多目标二人零和矩阵对策的线性规划方法。最后以数例说明本文提出的方法。结果表明该方法能方便地得到对策的均衡策略和均衡解。     

不确定偏好序下的双边匹配博弈

针对带有不确定偏好序的双边匹配问题,现有方法大都仅注重整体收益之和,忽略了参与人的个体收益以及在交互选择中的策略运用.基于最大满意度准则,给出不确定序下的收益（满意度）矩阵的推导过程;然后,从个体理性视角,结合矩阵博弈的思想构建一种兼顾整体和个体收益的博弈匹配优化模型,并证明模型最优解满足纳什均衡.最后,进一步探讨各种策略选择及其优劣分析.     

Robust game theory

We present a distribution-free model of incomplete-information games, both with and without private information, in which the players use a robust optimization approach to contend with payoff uncertainty. Our ``robust game' model relaxes the assumptions of Harsanyi's Bayesian game model, and provides an alternative distribution-free equilibrium concept, which we call ``robust-optimization equilibrium,' to that of the ex post equilibrium. We prove that the robust-optimization equilibria of an incomplete-information game subsume the ex post equilibria of the game and are, unlike the latter, guaranteed to exist when the game is finite and has bounded payoff uncertainty set. For arbitrary robust finite games with bounded polyhedral payoff uncertainty sets, we show that we can compute a robust-optimization equilibrium by methods analogous to those for identifying a Nash equilibrium of a finite game with complete information. In addition, we present computational results. The research of the author was partially supported by a National Science Foundation Graduate Research Fellowship and by the Singapore-MIT Alliance. The research of the author was partially supported by the Singapore-MIT Alliance.     

Quitting games – An example

Quitting games are multi-player sequential games in which, at every stage, each player has the choice between continuing and quitting. The game ends as soon as at least one player chooses to quit; each player i then receives a payoff r _S ⁱ, which depends on the set S of players that did choose to quit. If the game never ends, the payoff to each player is zero.? We exhibit a four-player quitting game, where the “simplest” equilibrium is periodic with period two. We argue that this implies that all known methods to prove existence of an equilibrium payoff in multi-player stochastic games are therefore bound to fail in general, and provide some geometric intuition for this phenomenon. Received: October 2001     

Project screening with tiered evaluation

We study a Bayesian game of two-sided incomplete information in which an agent, who owns a project of unknown quality, considers proposing it to an evaluator, who has the choice of whether or not to accept it. There exist two distinct tiers of evaluation that differ in the benefits they deliver to the agent upon acceptance of a project. The agent has to select the tier to which the project is submitted for review. Making a proposal incurs a cost on the agent in the form of a submission cost. We examine the effect of changes in the payoff parameters at the two tiers of evaluation on the efficiency of the equilibrium outcome. We show that changes in these parameters that are aimed at increasing the level of self-screening exerted by the agent do not necessarily have beneficial effects either on the quality of projects submitted for review or on the quality of projects that are implemented. From a methodological viewpoint, our paper proposes a novel method of performing comparative statics in games whose equilibria are defined by a system of equations with no closed-form solution.     

Risk and quality control in a supply chain: competitive and collaborative approaches

This paper provides a quantitative and comparative economic and risk approach to strategic quality control in a supply chain, consisting of one supplier and one producer, using a random payoff game. Such a game is first solved in a risk-neutral framework by assuming that both parties are competing with each other. We show in this case that there may be an interior solution to the inspection game. A similar analysis under a collaborative framework is shown to be trivial and not practical, with a solution to the inspection game being an ‘all or nothing’ solution to one or both the parties involved. For these reasons, the sampling random payoff game is transformed into a Neyman–Pearson risk constraints game, where the parties minimize the expected costs subject to a set of Neyman–Pearson risk (type I and type II) constraints. In this case, the number of potential equilibria can be large. A number of such solutions are developed and a practical (convex) approach is suggested by providing an interior (partial sampling) solution for the collaborative case. Numerical examples are developed to demonstrate the procedure used. Thus, unlike theoretical approaches to the solution of strategic quality control random payoff games, the approach we construct is both practical and consistent with the statistical risk Neyman–Pearson approach.     

NATURAL RESOURCE EXPLOITATION UNDER COMMON PROPERTY RIGHTS

ABSTRACT. Renewable natural resources such as ground‐water, pastures and fisheries are often governed bycommon propertyrights in which members of a group jointlyown the exclusive use of the resource. We develop a formal model of a common propertycontract based on differential game theory and then use the model to examine (i) the incentives of individual users of the common resource; (ii) the resulting harvest and stock time paths; (iii) the local stabilityof the steady state; and (iv) the steadystate comparative statics. Moreover, we compare the qualitative properties of the common propertyregime to those generated under perfectlydefined private rights and open access. We show how common prop‐ertyownership of natural resources can generate rent and be a second‐best solution when private propertyrights are costly to establish.     

Naive audience and communication bias

We introduce the possibility that the receiver naively believes the sender’s message in a game of information transmission with partially aligned objectives. We characterize an equilibrium in which the communication language is inflated, the action taken is biased, and the information transmitted is more precise than in the benchmark fully-strategic model. We provide comparative statics results with respect to the amount of asymmetric information, the proportion of naive receivers, and the size of the sender’s bias. As the state space grows unbounded, the equilibrium converges to the fully-revealing equilibrium that results in the limit case with unbounded state space.      

连续区间策略下二人零和对策问题研究

考虑连续区间策略下的二人零和对策问题,研究其均衡策略的存在性。首先分析了完全信息下的二人零和对策问题,证明了该问题均衡策略的存在性并给出求解方法。然后进一步研究了收益函数不确定的不完全信息二人零和对策问题,在各局中人都认为对方是风险厌恶型的假设下,分析该类对策纯策略均衡的存在性,并通过研究纯策略均衡存在的充要条件给出判断并寻找纯策略均衡解的方法。最后给出一个数值算例,验证本文所提出方法的可行性。     

Nash bargaining solution under externalities

We define a Nash bargaining solution (NBS) of partition function games. Based on a partition function game, we define an extensive game, which is a propose–respond sequential bargaining game where the rejecter of a proposal exits from the game with some positive probability. We show that the NBS is supported as the expected payoff profile of any stationary subgame perfect equilibrium (SSPE) of the extensive game such that in any subgame, a coalition of all active players forms immediately. We provide a necessary and sufficient condition for such an SSPE to exist. Moreover, we consider extensions to the cases of nontransferable utilities, time discounting and multiple-coalition formation.     

Warm-glow giving in networks with multiple public goods

This paper explores a voluntary contribution game in the presence of warm-glow effects. There are many public goods and each public good benefits a different group of players. The structure of the game induces a bipartite network structure, where players are listed on one side and the public good groups they form are listed on the other side. The main result of the paper shows the existence and uniqueness of a Nash equilibrium. The unique Nash equilibrium is also shown to be asymptotically stable. Then the paper provides some comparative statics analysis regarding pure redistribution, taxation and subsidies. It appears that small redistributions of wealth may sometimes be neutral, but generally, the effects of redistributive policies depend on how public good groups are related in the contribution network structure.     

Robust Multiple Objective Game Theory

In this paper, we propose a distribution-free model instead of considering a particular distribution for multiple objective games with incomplete information. We assume that each player does not know the exact value of the uncertain payoff parameters, but only knows that they belong to an uncertainty set. In our model, the players use a robust optimization approach for each of their objective to contend with payoff uncertainty. To formulate such a game, named “robust multiple objective games” here, we introduce three kinds of robust equilibrium under different preference structures. Then, by using a scalarization method and an existing result on the solutions for the generalized quasi-vector equilibrium problems, we obtain the existence of these robust equilibria. Finally, we give an example to illustrate our model and the existence theorems. Our results are new and fill the gap in the game theory literature.     

Nash equilibria of finitely repeated games

Under weak conditions, any feasible and individually rational payoff vector of a one-shot game can be approximated by the average payoff in a Nash equilibrium of a finitely repeated game with a long enough horizon.     

约束形式下广义最大元Nash均衡的存在性

运用广义最大元方法在非传递性偏好下给出了博弈均衡的存在性定理,推广了一些经典的博弈均衡存在性定理.在文中介绍策略式博弈的Nash均衡具有宽泛的条件,在微观经济理论中有广泛的应用.