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.     

Stationary and nonstationary strategies in Hotelling's model of spatial competition with repeated pricing decisions

This paper examines Hotelling's model of location with linear transportation cost. Existence of pure strategy subgame perfect equilibria in the infinitely repeated price game with fixed locations is proved. These subgame perfect equilibria have a stick and carrot structure. Given firm locations, there are discount factors sufficiently high that there is a subgame perfect equilibrium with a two-phase structure. Given the discount factors, there are stationary subgame perfect equilibria for a wide range of locations. However, for some pairs of location, no symmetric simple penal code exists, all subgame perfect profiles are nonstationary, and there is only one seller in the market in infinitely many periods. Received July 1996/Final version May 1998     

Location of an undesirable facility on a network: A bargaining approach

We examine a model where, on a line network, individuals collectively choose the location of an undesirable public facility through bargaining with the unanimity rule. We show the existence of a stationary subgame perfect equilibrium and the characterization of stationary subgame perfect equilibria when the discount factor is sufficiently large. Furthermore, we show that as the discount factor tends to 1, the equilibrium location can converge to a location that is least desirable according to both the Benthamite and Rawlsian criteria.     

Stationary perfect equilibria of an n-person noncooperative bargaining game and cooperative solution concepts

This paper characterizes the stationary (subgame) perfect equilibria of an n-person noncooperative bargaining model with characteristic functions, and provides strategic foundations of some cooperative solution concepts such as the core, the bargaining set and the kernel. The contribution of this paper is twofold. First, we show that a linear programming formulation successfully characterizes the stationary (subgame) perfect equilibria of our bargaining game. We suggest a linear programming formulation as an algorithm for the stationary (subgame) perfect equilibria of a class of n-person noncooperative games. Second, utilizing the linear programming formulation, we show that stationary (subgame) perfect equilibria of n-person noncooperative games provide strategic foundations for the bargaining set and the kernel.     

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     

Hotelling’s location model with negative network externalities

We study a variation of Hotelling’s location model in which consumers choose between firms based on travel distances as well as the number of consumers visiting each firm. The model in which the network externality is the same for all firms was proposed by Kohlberg (Econ Lett 11:211–216, 1983), who claims that no equilibrium exists for more than two firms. We assume the network effects to be linear and, in contrast to the claim in Kohlberg (Econ Lett 11:211–216, 1983), derive a condition under which a subgame perfect Nash equilibrium exists for four and six firms. Moreover, we show that for more than two firms the equilibrium locations of the firms are different from the equilibrium locations in Hotelling’s location model. Our results suggest that a subgame perfect Nash equilibrium exists if and only if the number of firms is even. We also provide examples of subgame perfect equilibria in which the network externality is different for some of the firms.     

Cournot–Walras equilibrium as a subgame perfect equilibrium

In this paper, we investigate the problem of the strategic foundation of the Cournot–Walras equilibrium approach. To this end, we respecify à la Cournot–Walras the mixed version of a model of simultaneous, noncooperative exchange, originally proposed by Lloyd S. Shapley. We show, through an example, that the set of the Cournot–Walras equilibrium allocations of this respecification does not coincide with the set of the Cournot–Nash equilibrium allocations of the mixed version of the original Shapley’s model. As the nonequivalence, in a one-stage setting, can be explained by the intrinsic two-stage nature of the Cournot–Walras equilibrium concept, we are led to consider a further reformulation of the Shapley’s model as a two-stage game, where the atoms move in the first stage and the atomless sector moves in the second stage. Our main result shows that the set of the Cournot–Walras equilibrium allocations coincides with a specific set of subgame perfect equilibrium allocations of this two-stage game, which we call the set of the Pseudo–Markov perfect equilibrium allocations. We would like to thank Pierpaolo Battigalli, Marcellino Gaudenzi, and an anonymous referee for their comments and suggestions.     

考虑损失厌恶行为与谈判破裂的Rubinstein谈判博弈研究

本文考虑具有损失厌恶行为与破裂风险的Rubinstein谈判博弈。首先构建子博弈完美均衡,并证明子博弈完美均衡的存在性及唯一性。然后分析子博弈完美均衡的性质,结果表明:参与人受益于对手的损失厌恶行为,而因自身具有损失厌恶行为遭受损失;谈判破裂概率对均衡结果的影响取决于贴现因子与参与人的损失厌恶系数;当谈判破裂的概率趋于零时,极限均衡结果收敛于经典的Rubinstein谈判博弈结果。最后建立了与非对称Nash谈判解的关系,其中参与人的议价能力与自身的损失厌恶水平呈负相关性,与对手的损失厌恶水平呈正相关性;参与人的议价能力依赖于谈判破裂概率与出价时间间隔的比值。     

带有网络外部性的动态寡头垄断定价

给出了带有网络外部性的两阶段寡头垄断定价模型,并用博弈论方法求解.通过与带有网络外部性的完全垄断定价模型的比较,得出重要结论:在网络外部性足够大的情况下,①寡头竞争情况下与完全垄断下情况一样,“科斯假设”将得到克服,均衡定价将呈现先低后高的情况.②对于完全垄断厂商来说,网络外部性k的增加能够增加其利润,但对于寡头竞争的企业来说,正好相反,k的增加将导致其利润的下降.     

贸易自由化背景下幼稚产业的最优保护关税

本构造了一个完全信息二次线性动态对策模型，分析面临贸易自由化时，对一个幼稚产业的最优保护进口关税，给出了符合子博弈精炼均衡的对策解。并以中国轿车工业的实际数据进行实证分析，考虑在贸易自由化的背景下，轿车产品的最优总体平均进口保护关税税率。     

Complementarity Enhanced Nash’s Mappings and Differentiable Homotopy Methods to Select Perfect Equilibria

Journal of Optimization Theory and Applications - To extend the concept of subgame perfect equilibrium to an extensive-form game with imperfect information but perfect recall, Selten (Int J Game...     

Sequential share bargaining

This paper presents a new extension of the Rubinstein-St?hl bargaining model to the case with n players, called sequential share bargaining. The bargaining protocol is natural and has as its main feature that the players’ shares in the surplus are determined sequentially rather than simultaneously. The protocol also assumes orderly voting, a restriction on the order in which players respond to a proposal. The bargaining protocol requires unanimous agreement for proposals to be implemented. Unlike all existing bargaining protocols with unanimous agreement, the resulting game has unique subgame perfect equilibrium utilities for any value of the discount factor. The result builds on the analysis of so-called one-dimensional bargaining problems. We show that also one-dimensional bargaining problems have unique subgame perfect equilibrium utilities for any value of the discount factor.     

The simple geometry of perfect information games

Perfect information games have a particularly simple structure of equilibria in the associated normal form. For generic such games each of the finitely many connected components of Nash equilibria is contractible. For every perfect information game there is a unique connected and contractible component of subgame perfect equilibria. Finally, the graph of the subgame perfect equilibrium correspondence, after a very mild deformation, looks like the space of perfect information extensive form games.     

On the notion of perfect Bayesian equilibrium

Often, perfect Bayesian equilibrium is loosely defined by stating that players should be sequentially rational given some beliefs in which Bayes rule is applied “whenever possible.” We argue that there are situations in which it is not clear what “whenever possible” means. Then we provide an elementary definition of perfect Bayesian equilibrium for general extensive games that refines both weak perfect Bayesian equilibrium and subgame perfect equilibrium.     

Dynamic pricing with uncertain production cost: An alternating-move approach

This article studies a two-firm dynamic pricing model with random production costs. The firms produce the same perishable products over an infinite time horizon when production (or operation) costs are random. In each period, each firm determines its price and production levels based on its current production cost and its opponent’s previous price level. We use an alternating-move game to model this problem and show that there exists a unique subgame perfect Nash equilibrium in production and pricing decisions. We provide a closed-form solution for the firm’s pricing policy. Finally, we study the game in the case of incomplete information, when both or one of the firms do not have access to the current prices charged by their opponents.     

Open versus closed loop capacity equilibria in electricity markets under perfect and oligopolistic competition

We consider two game-theoretic models of the generation capacity expansion problem in liberalized electricity markets. The first is an open loop equilibrium model, where generation companies simultaneously choose capacities and quantities to maximize their individual profit. The second is a closed loop model, in which companies first choose capacities maximizing their profit anticipating the market equilibrium outcomes in the second stage. The latter problem is an equilibrium problem with equilibrium constraints. In both models, the intensity of competition among producers in the energy market is frequently represented using conjectural variations. Considering one load period, we show that for any choice of conjectural variations ranging from perfect competition to Cournot, the closed loop equilibrium coincides with the Cournot open loop equilibrium, thereby obtaining a ‘Kreps and Scheinkman’-like result and extending it to arbitrary strategic behavior. When expanding the model framework to multiple load periods, the closed loop equilibria for different conjectural variations can diverge from each other and from open loop equilibria. We also present and analyze alternative conjectured price response models with switching conjectures. Surprisingly, the rank ordering of the closed loop equilibria in terms of consumer surplus and market efficiency (as measured by total social welfare) is ambiguous. Thus, regulatory approaches that force marginal cost-based bidding in spot markets may diminish market efficiency and consumer welfare by dampening incentives for investment. We also show that the closed loop capacity yielded by a conjectured price response second stage competition can be less or equal to the closed loop Cournot capacity, and that the former capacity cannot exceed the latter when there are symmetric agents and two load periods.     

A non-cooperative interpretation of the kernel

The purpose of the paper is to propose a bargaining game to interpret the kernel non-cooperatively. Based on the idea of the Davis-Maschler reduced game, a bilateral bargaining procedure is provided in our game model. We show that the set of all subgame perfect equilibrium outcomes of our non-cooperative game coincides with the kernel for transferable utility games.     

<Emphasis Type="Italic">O</Emphasis>(1) loop model with different boundary conditions and symmetry classes of alternating-sign matrices

This work is a continuation of our recent paper where we discussed numerical evidence that the numbers of the states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the O(1) loop model with periodic boundary conditions and an even number of sites. We give two new conjectures related to different boundary conditions: we suggest and numerically verify that the numbers of the half-turn symmetric states of the fully packed loop model with fixed pairing patterns coincide with the components of the ground state vector of the O(1) loop model with periodic boundary conditions and an odd number of sites and that the corresponding numbers of the vertically symmetric states describe the case of open boundary conditions and an even number of sites.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 2, pp. 284–292, February, 2005.