Correlated Equilibrium in Stochastic Games

We study the existence of uniform correlated equilibrium payoffs in stochastic games. The correlation devices that we use are either autonomous (they base their choice of signal on previous signals, but not on previous states or actions) or stationary (their choice is independent of any data and is drawn according to the same probability distribution at every stage). We prove that any n-player stochastic game admits an autonomous correlated equilibrium payoff. When the game is positive and recursive, a stationary correlated equilibrium payoff exists. Journal of Economic Literature Classification Numbers: C72, C73.     

Congestion Pricing and Learning in Traffic Network Games

A stochastic model describing the learning process and adaptive behavior of finitely many users in a congested traffic network with parallel links is used to prove convergence almost surely toward an efficient equilibrium for a related game. To prove this result, we assume that the social planner charges on every route the marginal cost pricing without knowing what is the efficient equilibrium. The result is a dynamic version of Pigou’s solution, where the implementation is made in a decentralized way and the information about players gathered by the social planner is minimal. Our result and setting may be extended to the general case of negative externalities.     

Socially Subjective Equilibrium in Strategic Form Games

This study provides a new framework and a new equilibrium concept, which are able to describe the situation where people have various images of the society and have various solution concepts for social outcomes, and where people accept the social outcomes. In socially subjective equilibrium, people have a coherence of their own norms in two senses. One is the consistency of the norm itself. Imagined outcomes should satisfy a certain (subjective) solution concept. The other is the consistency between the imagined outcomes and realized one. These are the main features of our equilibrium concept. This paper forms a part of my doctoral thesis, which is titled “On socially subjective equilibrium”. The first person I would like to thank is my direct supervisor Professor Ken Urai (Osaka University). I obtained a basic idea of the main concept of my doctoral thesis, that is, the solution concept scheme, from Professor Urai. I am grateful to Professor Hiroaki Nagatani (Osaka University) and Professor Ken-Ichi Shimomura (Kobe University), who monitored my works and took efforts in providing me with valuable comments on earlier versions of my thesis. I also obtained a fruitful advice from Professor Kenichi Amaya (Kobe University). Lastly, I specially thank to Kozo Shiraishi (Osaka University).     

Equilibrium Selection inn-Person Coordination Games

This paper investigates several approaches to equilibrium selection and the relationships between them. The class of games we study aren-person generalized coordination games with multiple Pareto rankable strict Nash equilibria. The main result is that all selection criteria select the same outcome (namely the risk dominant equilibrium) in two-person games, and that most equivalences break for games with more than two players. All criteria select the Pareto efficient equilibrium in voting games, of which pure coordination games are special cases.Journal of Economic LiteratureClassification Numbers: C70, C72, D82.     

On the Generic Finiteness of Equilibrium Outcomes in Plurality Games

In this paper we prove that for generic (noncooperative) voting games under plurality rule the set of equilibria that induce a mixed distribution over the outcomes (i.e., with two or more candidates elected with positive probability) is finite and, furthermore, each of these equilibria is regular. From that we deduce the finiteness of the set of equilibrium distributions over outcomes. Furthermore we offer an example (S. Govindan and A. McLennan, 1997, “On the Generic Finiteness of Equilibrium Outcome Distributions in Game Forms,” mimeo) that shows the impossibility of extending such results to a general framework, even just to voting games. Journal of Economic Literature Classification Numbers: C72, D72.     

Minimum-Effort Coordination Games: Stochastic Potential and Logit Equilibrium

This paper revisits the minimum-effort coordination game with a continuum of Pareto-ranked Nash equilibria. Noise is introduced via a logit probabilistic choice function. The resulting logit equilibrium distribution of decisions is unique and maximizes a stochastic potential function. In the limit as the noise vanishes, the distribution converges to an outcome that is analogous to the risk-dominant outcome for 2 × 2 games. In accordance with experimental evidence, logit equilibrium efforts decrease with increases in effort costs and the number of players, even though these parameters do not affect the Nash equilibria. Journal of Economic Literature Classification Numbers: C72, C92.     

Equilibrium Tariff Schedules In Commercial Policy Games Under Uncertainty

Abstract A partial two country equilibrium model is built in which two different exogenous random shocks may occur. the governments simultaneously choose tariff functions relating their specific tariff to the level of an observable variable (volume of trade or international price). In the case of a “volume of trade shock” the Nash equilibria of this game are more protectionist the larger the possible trade swings and autarky is always an equilibrium outcome. In the case of a “terms of trade shock”, constant tariffs, at their Nash equilibrium in specific tariff levels are the only sensible equilibrium outcome.     

On the Uniqueness of Equilibrium in Cournot Oligopoly and Other Games

In an average surplus sharing game, such as a Cournot oligopoly, a group of agents share a production process. Each contributes an amount of input to the process, and output is divided in proportion to the amount of input contributed. Uniqueness of the equilibrium is needed for any type of comparative static analysis. However, general uniqueness results for concave games have restrictive assumptions on preferences and technology; specifically, the conditions needed for uniqueness become more difficult to meet as the number of players increases. A new theorem for uniqueness with easily interpretable conditions is given which is independent of the number of players.Journal of Economic LiteratureClassification Numbers: C70, C72, D43.     

Pure-Strategy ε-Nash Equilibrium inn-Person Nonzero-Sum Discontinuous Games

In this paper we considern-person nonzero-sum games where the strategy spaces of players are compact subsets ofR^s. The main result states that if the payoff functions are semicontinuous and strongly quasi-concave then an ε-Nash equilibrium in pure strategies exists for every positive ε.Journal of Economic LiteratureClassification Number: C72.     

Equilibrium in Justifiable Strategies: A Model of Reason-based Choice in Extensive-form Games

I explore the idea that people care about the justifiability of their decisions in the context of two-person extensive games. Each player justifies his strategy  s  with a belief  b  of the opponent's strategy, which is consistent with the play path and maximally plausible (according to some exogenous criterion). We say that  s  is justifiable if against the ex post criticism that some other strategy  s'  outperforms  s  against  b  , the player can argue that playing  s'  would have exposed him to similar criticism in the opposite direction. Under a simplicity-based plausibility criterion, this concept implies systematic departures from maximizing behaviour in familiar games.     

期权博弈的分类及其在不完全信息下的均衡策略研究

期权博弈的分类与均衡策略研究是进行期权博弈模型研究,为企业在不同的竞争性投资实践中提供科学决策的基础与根本。首先从实物期权的种类和竞争特性出发对期权博弈进行了分类与界定。然后,在不完全信息条件下,重点研究了占优型实物期权博弈均衡策略。无论是在高成本或低成本类型下,占优型企业均会以低成本的身份选择最佳投资时机和最佳垄断产量进入市场生产、成为市场的领导者;在观察到领导者行动策略的基础上,追随者按实物期权方法的投资决策基本规则确定其进入市场的最佳投资时机;随后,领导者与追随者按照精炼贝耶斯纳什均衡产量进行生产,共同获得市场均衡收益。     

Evolution of Beliefs and the Nash Equilibrium of Normal Form Games

The paper formulates a simple two-person model of learning with pattern recognition and discusses its implications. In particular, it focuses on the asymptotic behavior of players' beliefs when the game has a mixed-strategy Nash equilibrium.Journal of Economics LiteratureClassification Numbers: C72, D83.     

Working and Shirking: Equilibrium in Public-Goods Games with Overlapping Generations of Players

In overlapping-generations models of public-goods provision,in which the contribution decision is binary and lifetimes arefinite, the set of symmetric subgame-perfect equilibria canbe categorized into three types: seniority equilibria, in whichplayers contribute (effort) until a predetermined age and thenshirk thereafter; dependency equilibria, in which players initiallyshirk, then contribute for a set number of periods, then shirkfor the remainder of their lives; and sabbatical equilibria,in which players alternately contribute and shirk for periodsof varying length before entering a final stage of shirking.In a world without discounting we establish conditions for equilibriumand demonstrate that for any dependency equilibrium there isa seniority equilibrium that Pareto dominates it ex ante. Weproceed to characterize generational preferences over alternativeseniority equilibria. We explore the aggregation of these preferencesby embedding the public-goods provision game in a voting frameworkand solving for the majority-rule equilibria. In this way wecan think of political processes as providing one natural frameworkfor equilibrium selection in the original public-goods provisiongame.     

Existence and Uniqueness of Nash Equilibrium in Electoral Competition Games: The Hybrid Case

This paper analyzes the traditional unidimensional, two‐party electoral competition game when parties have mixed motivations, in the sense that they are interested in winning the election, but also in the policy implemented after the contest. In spite of having discontinuous payoffs, this game, referred to as the hybrid election game, is shown to be payoff secure and reciprocally upper semi‐continuous. Conditional payoffs, however, are not quasi‐concave. Hence, the existence of a pure strategy Nash equilibrium (psne ) is ensured only if parties have homogenous interests in power. In that case, an equilibrium not only exists, but it is also unique. Instead, if parties have heterogeneous motivations, depending upon the relationship between the electoral uncertainty, the aggregate opportunism, and its distribution across parties, a psne may or may not exist. The mixed extension, however, is always better reply secure. Therefore, a mixed strategy Nash equilibrium does indeed exist.     

基于政府型强互惠的共享意义制度化的均衡与内卷

政府型强互惠将那些共享意义的习惯、习俗以具体的形式固定下来,实现制度化。当制度演化收敛于某一均衡点时,群体成员对于现行的规范体系不再有异动的要求,于是制度在均衡状态下表现为被简单的遗传复制,从而强互惠的政府就无须再对这些制度的强互惠投入成本,制度演化也自发地达成了均衡状态。在自发式内卷和强互惠式内卷两种力量共同作用下,制度会呈现长期低效率的锁定状态。     

Congestion management in power systems

In liberalized power systems, generation and transmission services are unbundled, but remain tightly interlinked. Congestion management in the transmission network is of crucial importance for the efficiency of these inter-linkages. Different regulatory designs have been suggested, analyzed and followed, such as uniform zonal pricing with redispatch or nodal pricing. However, the literature has either focused on the short-term efficiency of congestion management or specific issues of timing investments. In contrast, this paper presents a generalized and flexible economic modeling framework based on a decomposed inter-temporal equilibrium model including generation, transmission, as well as their inter-linkages. The model covers short-run operation and long-run investments and hence, allows to analyze short and long-term efficiency of different congestion management designs that vary with respect to the definition of market areas, the regulation and organization of TSOs, the way of managing congestion besides grid expansion, and the type of cross-border capacity allocation. We are able to identify and isolate implicit frictions and sources of inefficiencies in the different regulatory designs, and to provide a comparative analysis including a benchmark against a first-best welfare-optimal result. To demonstrate the applicability of our framework, we calibrate and numerically solve our model for a detailed representation of the Central Western European (CWE) region, consisting of 70 nodes and 174 power lines. Analyzing six different congestion management designs until 2030, we show that compared to the first-best benchmark, i.e., nodal pricing, inefficiencies of up to 4.6% arise. Inefficiencies are mainly driven by the approach of determining cross-border capacities as well as the coordination of transmission system operators’ activities.     

Discontinuous Payoffs, Shared Resources, and Games of Fiscal Competition: Existence of Pure Strategy Nash Equilibrium

We define a class of games with discontinuous payoffs that we call shared resource games and establish a pure strategy Nash equilibrium existence theorem for these games. We then apply this result to a canonical game of fiscal competition for mobile capital. Other applications are also discussed. Our result for the mobile capital game holds for any finite number of regions, permits general preferences over private and public goods, and does not assume that production technologies have a particular functional form, or are identical in all regions, or satisfy the Inada condition at zero.     

Congestion effects in a public-good economy

This paper considers a public-good economy with congestion, where participants jointly produce a public good from input of a private good. This economic model gives rise to a transferable-utility game, the profit game, that depends on consumer preferences and a congestion parameter. The simplicity of the game allows the maximum level of congestion that guarantees the nonemptiness of the core of the economy to be determined. It is known that the sustainability of the Lindahl equilibrium in the core of the economy depends on the distribution of profits. In this paper two distributions of profits are compared: the Lindahl solution and the marginal-contribution solution. The latter is more often in the core than the Lindahl solution which in turn Lorenz-dominates the marginal-contribution solution.