INACCESSIBLE CONTINUOUSLY STABLE STRATEGIES

ABSTRACT. The evolutionary stability concepts continuously stable strategies (CSS) and evolutionarily stable neighborhood invader strategies (ESNIS) share two properties in common. First, they are both evolutionarily stable strategies (ESS). Secondly, given any strategy in the close neighborhood of the CSS or ESNIS, there are some strategies that are closer to the CSS or ESNIS that can invade it. An ESNIS is a CSS but the converse is not true in general. We examine evolutionary adaptive dynamics in the neighborhood of a CSS that is not an ESNIS. We show that if an evolutionary game possesses a CSS which is not an ESNIS, the succession of strategies mediated by natural selection become arbitrarily close to the CSS but the precise value of the CSS cannot be attained unless the CSS is the first strategy to invade into the environment and is henceforth never perturbed. Thus if evolution does not start with the CSS that is not an ESNIS, we will have a phenomenon of bounded evolutionary succession that does not come to an end. The analysis is applied to a class of monomorphic population evolutionary game models in which species ecological interaction is modeled by the Lotka‐Volterra equations.     

Solutions for some bargaining games under the Harsanyi-Selten solution theory,part II: Analysis of specific bargaining games

Part II of the paper (for Part I see Harsanyi (1982)) describes the actual solutions the Harsanyi-Selten solution theory provides for some important classes of bargaining games, such as unanimity games; trade between one seller and several potential buyers; and two-person bargaining games with incomplete information on one side or on both sides. It also discusses some concepts and theorems useful in computing the solution; and explains how our concept of risk dominance enables us to analyze game situations in terms of some intuitively very compelling probabilistic (subjective-probability) considerations disallowed by classical game theory.     

多重均衡选择中的风险占优与混合策略

均衡选择理论是博弈理论的重要组成部分.风险占优均衡是人们经济决策或行为的一个主要结果.利用混合策略及其性质和“抵制”的概念,“支持”了海萨尼和泽尔腾用公理定义的风险占优概念,且具体给出了识别风险占优均衡的标准和方法,并把它们推广到对称博弈中去.最后对均衡占优的直觉概念和风险占优相冲突的一些博弈进行了类似的讨论.     

Threat bargaining games with a variable population

In this paper we establish links between desirable properties satisfied by familiar solutions to bargaining games with a variable population and the Nash equilibrium concept for threat bargaining games. We introduce three new concepts for equilibrium threat strategies called strategic stability, strategic monotonicity with respect to changes in the number of agents and strategic constancy. Our primary objective in this paper is to show that familiar assumptions satisfied by bargaining games with a variable population yield equilibrium threat strategies which satisfies in a very natural way the concepts we have introduced.     

Social systems analysis II

We argue that there are 4 basic solution concepts for 2 × 2 symmetric games and corresponding to these, 4 basic human interactions and 4 types of societies. We propose a model in which the type of interaction is predicted by independence, inequality of power, communication, and mutuality of interests. We prove theorems classifying Moulin's inessential games in the case of an interior Nash equilibrium and argue that this explains coalition formation. We discuss classification of socially significant ideologies.     

A gradient projection method for solving continuous games

This paper develops a procedure for numerically solving continuous games (and also matrix games) using a gradient projection method in a general Hilbert space setting. First, we analyze the symmetric case. Our approach is to introduce a functional which measures how far a strategy deviates from giving zero value (i.e., how near the strategy is to being optimal). We then incorporate this functional into a nonlinear optimization problem with constraints and solve this problem using the gradient projection algorithm. The convergence is studied via the corresponding steepest-descent differential equation. The differential equation is a nonlinear initial-value problem in a Hilbert space; thus, we include a proof of existence and uniqueness of its solution. Finally, nonsymmetric games are handled using the symmetrization techniques of Ref. 1.     

Local dominance and local recombination in MOEAs on 0/1 multiobjective knapsack problems

This work studies and compares the effects on performance of local dominance and local recombination applied with different locality in multiobjective evolutionary algorithms on combinatorial 0/1 multiobjective knapsack problems. For this purpose, we introduce a method that creates a neighborhood around each individual and assigns a local dominance rank after alignment of the principle search direction of the neighborhood by using polar coordinates in objective space. For recombination a different neighborhood determined around a random principle search direction is created. The neighborhood sizes for dominance and recombination are separately controlled by two different parameters. Experimental results show that the optimum locality of dominance is different from the optimum locality of recombination. Additionally, it is shown that the performance of the algorithm that applies local dominance and local recombination with different locality is significantly better than the performance of algorithms applying local dominance alone, local recombination alone, or dominance and recombination globally as conventional approaches do.     

Dynamic stability in symmetric extensive form games

Dynamic stability under the replicator dynamic of evolutionary game theory is investigated for certain symmetric extensive form games whose subgame structure exhibits a high degree of decomposability. It is shown that a pervasive equilibrium strategy is locally asymptotically stable (l.a.s.) if and only if it is given by backwards induction applied to the l.a.s. pervasive equilibria of the subgames and their corresponding truncations. That is, this dynamic backwards induction procedure provides a rational basis on which to predict the evolutionary outcome of the replicator dynamic for these symmetric games.     

Replication invariance on NTU games

Two concepts of replication (conflictual and non-conflictual) are extended from the class of pure bargaining games to the class of NTU games. The behavior of the Harsanyi, Shapley NTU, Egalitarian and Maschler-Owen solutions of the replica games is compared with that of the Nash and Egalitarian solutions in pure bargaining games. Received June 1995/Final version February 2000     

Sufficient conditions for Nash equilibria inN-person games over reflexive Banach spaces

Sufficient conditions are obtained for the existence of Nash equilibrium points inN-person games when the strategy sets are closed, convex subsets of reflexive Banach spaces. These conditions require that each player's cost functional is convex in that player's strategy, weakly continuous in the strategies of the other players, weakly lower semicontinuous in all strategies, and furthermore satisfies a coercivity condition if any of the strategy sets is unbounded. The result is applied to a class of linear-quadratic differential games with no information, to prove that equilibrium points exist when the duration of these games is sufficiently small.This work was supported by a Commonwealth of Australia, Postgraduate Research Award.     

The reactive bargaining set for cooperative games

We introduce a new bargaining set for cooperative games in characteristic function form, and investigate its structure and properties. We prove that the new bargaining set is not empty. In fact, we show that it contains the kernel and is contained in the classical bargaining set ${\mathcal{M}^i_1}$ , and we further prove that it consists of the unique symmetric vector for the class of simple majority games.     

Nash refinement of equilibria

A method for choosing equilibria in strategic form games is proposed and axiomatically characterized. The method as well as the axioms are inspired by the Nash bargaining theory. The method can be applied to existing refinements of Nash equilibrium (e.g., perfect equilibrium) and also to other equilibrium concepts, like correlated equilibrium.The authors thank the reviewers for their comments, which led to an improvement of the paper.     

The semireactive bargaining set of a cooperative game

The semireactive bargaining set, a solution for cooperative games, is introduced. This solution is in general a subsolution of the bargaining set and a supersolution of the reactive bargaining set. However, on various classes of transferable utility games the semireactive and the reactive bargaining set coincide. The semireactive prebargaining set on TU games can be axiomatized by one-person rationality, the reduced game property, a weak version of the converse reduced game property with respect to subgrand coalitions, and subgrand stability. Furthermore, it is shown that there is a suitable weakening of subgrand stability, which allows to characterize the prebargaining set. Replacing the reduced game by the imputation saving reduced game and employing individual rationality as an additional axiom yields characterizations of both, the bargaining set and the semireactive bargaining set. Received September 2000/Revised version June 2001     

Some results on cooperative interval games

Uncertainty is a daily presence in the real world. It affects our decision-making and may have influence on cooperation. On many occasions, uncertainty is so severe that we can only predict some upper and lower bounds for the outcome of our actions, i.e. payoffs lie in some intervals. A suitable game theoretic model to support decision-making in collaborative situations with interval data is that of cooperative interval games. Solution concepts that associate with each cooperative interval game sets of interval allocations with appealing properties provide a natural way to capture the uncertainty of coalition values into the players’ payoffs. In this paper, the relations between some set-valued solution concepts using interval payoffs, namely the interval core, the interval dominance core, the square interval dominance core and the interval stable sets for cooperative interval games, are studied. It is shown that the interval core is the unique stable set on the class of convex interval games.     

Game theoretic models for climate change negotiations

Negotiations to reduce greenhouse gas accumulation in the atmosphere are modeled as extensive games of perfect information. Various solution concepts, such as Nash equilibrium, reaction function equilibrium, correlated equilibrium and bargaining solutions are applied, analyzed and computed. Special reduction techniques are used when the size of the game tree becomes excessive. A new solution concept, the tree-correlated equilibrium is also introduced. Main features of an Excel add-in designed to compute various solutions are briefly described and a sample policy analysis for a special negotiating scenario is discussed.     

An axiomatization of the weighted NTU value

Non-symmetric generalizations of the non-transferable utility (NTU) are defined and characterized axiomatically. The first of these is a weighted NTU value that is identical to the (symmetric) NTU value when players have the same weights. On the class of transferable utility games, this weighted NTU value coincides with the weighted Shapley value and on the pure bargaining games it coincides with the non-symmetric Nash bargaining solution. A further extension, the random order NTU value, is also defined and axiomatized and its relationship to the core is discussed.     

Nonzero-sum differential games with bargaining solutions

Nash's bargaining solution for finite games is extended to differential games with nonzero-sum integral payoffs. Sufficient conditions for the optimality of a strategy pair are established. An example is given.     

Cores and related solution concepts for multi-choice games

A multi-choice game is a generalization of a cooperative game in which each player has several activity levels. Cooperative games form a subclass of the class of multi-choice games.This paper extends some solution concepts for cooperative games to multi-choice games. In particular, the notions of core, dominance core and Weber set are extended. Relations between cores and dominance cores and between cores and Weber sets are extensively studied. A class of flow games is introduced and relations with non-negative games with non-empty cores are investigated.     

I-FTOP同构于I-FRN

首先引入了I-fuzzy远域系和I-fuzzy远域空间的概念,然后构造了I-fuzzy远域空间和它们的连续映射的范畴,将此记作I-FRN.并进一步证明了I-FRN同构于I-FTOP.     

Symmetric versus asymmetric equilibria in symmetric supermodular games

This paper investigates the general properties of symmetric n-player supermodular games with complete-lattice action spaces. In particular, we examine the extent to which all pure strategy Nash equilibria tend to be symmetric for the general case of multi-dimensional strategy spaces. As asymmetric equilibria are possible even for strictly supermodular games, we investigate whether some symmetric equilibrium would always Pareto dominate all asymmetric equilibria. While this need not hold in general, we identify different sufficient conditions, each of which guarantees that such dominance holds: 2-player games with scalar action sets, uni-signed externalities, identical interests, and superjoin payoffs. Various illustrative examples are provided. Finally, some economic applications are discussed. The first version of this paper was completed while M. Jakubczyk and M. Knauff were visiting junior scholars at CORE, Louvain-la-Neuve, Belgium, financed through the Marie-Curie Early Stage Training program of the European Union (under contract no HPMT-CT-2001-00327), which is hereby gratefully acknowledged. The presentation of the revised version of this paper has benefitted from detailed and careful suggestions by two anonymous referees and William Thomson (as editor) of this Journal.