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An analysis is given of the character of games of chance and games of skill. It is shown that every game is influenced by stochastic effects. Whether a game should be classified as a game of pure skill or as a game of chance depends on the rules of the game, on the evaluation of the outcomes of the game and on the possibilities the player has by applying his skill to cope with the random effects of the particular game situations.     

Coalitional games with veto players: Consistency, monotonicity and Nash outcomes

Following Dagan et al. [Dagan, N., Volij, O., Serrano, R. (1997). A non-cooperative view on consistent bankruptcy rules, Games Econ. Behav. 18, 55–72], we construct an extensive form game for veto-balanced TU games in which a veto player is the proposer and the other players are responders. The set of Nash outcomes of this extensive form game is described, and compared to solutions of TU games such as the nucleolus, kernel and egalitarian core. We find necessary and sufficient conditions under which the nucleolus of the game is a Nash outcome.     

Strategic behavior in non-atomic games

In order to remedy the possible loss of strategic interaction in non-atomic games with a societal choice, this study proposes a refinement of Nash equilibrium, strategic equilibrium. Given a non-atomic game, its perturbed game is one in which every player believes that he alone has a small, but positive, impact on the societal choice; and a distribution is a strategic equilibrium if it is a limit point of a sequence of Nash equilibrium distributions of games in which each player’s belief about his impact on the societal choice goes to zero. After proving the existence of strategic equilibria, we show that all of them must be Nash. We also show that all regular equilibria of smooth non-atomic games are strategic. Moreover, it is displayed that in many economic applications, the set of strategic equilibria coincides with that of Nash equilibria of large finite games.     

Strategic complementarities and nested potential games

This paper reports that every finite game of strategic complementarities is a nested pseudo-potential game defined by Uno [Uno, H., 2007. Nested potential games. Economics Bulletin 3(17), 1–8] if the action set of each player is one-dimensional, except possibly for one player.     

Strong Nash equilibrium in games with common and complementary local utilities

A rather general class of strategic games is described where the coalitional improvements are acyclic and hence strong Nash equilibria exist: The players derive their utilities from the use of certain facilities; all players using a facility extract the same amount of local utility therefrom, which amount depends both on the set of users and on their actions, and is decreasing in the set of users; the ultimate utility of each player is the minimum of the local utilities at all relevant facilities. Two important subclasses are “games with structured utilities,” basic properties of which were discovered in 1970s and 1980s, and “bottleneck congestion games,” which attracted researchers’ attention quite recently. The former games are representative in the sense that every game from the whole class is isomorphic to one of them. The necessity of the minimum aggregation for the existence of strong Nash equilibria, actually, just Pareto optimal Nash equilibria, in all games of this type is established.     

Are “Anti-Folk Theorems” in repeated games nongeneric?

Folk Theorems in repeated games hold fixed the game payoffs, while the discount factor is varied freely. We show that these results may be sensitive to the order of limits in situations where players move asynchronously. Specifically, we show that when moves are asynchronous, then for a fixed discount factor close to one there is an open neighborhood of games which contains a pure coordination game such that every Perfect equilibrium of every game in the neighborhood approximates to an arbitrary degree the unique Pareto dominant payoff of the pure coordination game.     

A noncooperative approach to the Mas-Colell bargaining set

We propose an extensive form game to give a noncooperative interpretation of the Mas-Colell bargaining set for transferable utility games. Based on the objection and counterobjection in the sense of the Mas-Colell bargaining set, a bilateral negotiation is designed in our model. We show that the equilibrium outcomes of our extensive form game coincide with the Mas-Colell bargaining set in the supperadditive environments.     

The Theory of Socially Embedded Games: The Mathematics of Social Relationships,Rule Complexes,and Action Modalities

In their classic work, Von Neumann and Morgensterndefined a game as simply the totality of the rules which describe it. Theydid not, however, elaborate a theory of rules. Such considerations lead toconceptualizing rules and rule configurations as mathematical objects, specifyingthe principles for combining rules, developing the theory of revising,replacing, and, in general transforming rules and rule complexes. Themathematics is based on contemporary developments at the interface ofmathematics, logic, and computer science. This article, drawing on themathematical theory of rules and rule complexes, extends and generalizes gametheory (GGT). The theory of rule complexes is used to conceptualize andanalyze diverse social relationships, roles, and games as particulartypes of rule complexes. A social role, for instance, is the major basisof an individual's action in a game. It consists of at least four majorcomponents – which are mathematical objects – in the determinationof action: value complex, model of reality (including beliefs and knowledgebases), a repertoire of acts, routines, programs, and strategies, and modalities,role-specific algorithms for determininig or generating action in gamesettings. The article focuses on three types of action modality routineor habitual, normative, andinstrumental modalities. The theory: (1) provides a cultural/institutionalbasis for a theory of gameswhere games, social relationships, and rolesare formalized in terms of rule complexes; (2) explains human action as a formof rule application or rule-following action, which underlies allmodalities of action; (3) formulates the theory that actors construct an action or make choices amongalternative actions by making comparisons and judging similarity (ordissimilarity) between an option or options considered and their norms and values,and, in general, determine whether or not, and to what degree, a value,norm, or goal will be realized or satisfied; (4)reconceptualizes ``game' as a social form and makes a distinction between open and closed games.     

Equilibrium selection in games: the mollifier method

This paper introduces an embedding of a Nash equilibrium into a sequence of perturbed games, which achieves continuous differentiability of best responses by mollifying them over a continuously differentiable density with compact support (window size). Along any sequence with shrinking window size, the equilibria are single-valued whenever the function has a regular Jacobian and the set of equilibria where it is singular has measure zero. We achieve a further reduction of the equilibrium set by inserting within the embedding a procedure that eliminates the strict interior of equilibrium sets. The mollifier can be approximated consistently using kernel density regression, and we sketch a non-stationary stochastic optimization algorithm that uses this approximation and converges with probability one to an equilibrium of the original game.     

Evolving densities in continuous strategy games through particle simulations

Many cases of strategic interaction between agents involve a continuous set of choices. It is natural to model these problems as continuous space games. Consequently, the population of agents playing the game will be represented with a density function defined over the continuous set of strategy choices. Simulating evolutionary dynamics on continuous strategy spaces is a challenging problem. The classic approach of discretizing the strategy space is ineffective for multidimensional strategy spaces. We present a principled approach to simulation of adaptive dynamics in continuous space games using sequential Monte Carlo methods. Sequential Monte Carlo methods use a set of weighted random samples, also named particles to represent density functions over multidimensional spaces. Sequential Monte Carlo methods provide computationally efficient ways of computing the evolution of probability density functions. We employ resampling and smoothing steps to prevent particle degeneration problem associated with particle estimates. The resulting algorithm can be interpreted as an agent based simulation with elements of natural selection, regression to mean and mutation. We illustrate the performance of the proposed simulation technique using two examples: continuous version of the repeated prisoner dilemma game and evolution of bidding functions in first-price closed-bid auctions.     

On axiomatizations of the Shapley value for assignment games

We consider the problem of axiomatizing the Shapley value on the class of assignment games. It turns out that several axiomatizations of the Shapley value on the class of all TU-games do not characterize this solution on the class of assignment games. However, when considering an assignment game as a (communication) graph game where the game is simply the assignment game and the graph is a corresponding bipartite graph where buyers (sellers) are connected with sellers (buyers) only, we show that Myerson’s component efficiency and fairness axioms do characterize the Shapley value on the class of assignment games. Moreover, these two axioms have a natural interpretation for assignment games. Component efficiency yields submarket efficiency stating that the sum of the payoffs of all players in a submarket equals the worth of that submarket, where a submarket is a set of buyers and sellers such that all buyers in this set have zero valuation for the goods offered by the sellers outside the set, and all buyers outside the set have zero valuations for the goods offered by sellers inside the set. Fairness of the graph game solution boils down to valuation fairness stating that only changing the valuation of one particular buyer for the good offered by a particular seller changes the payoffs of this buyer and seller by the same amount.     

The testable implications of zero-sum games

We study collective choices from the revealed preference theory viewpoint. For every product set of individual actions, joint choices are called Nash-rationalizable if there exists a preference relation for each player such that the selected joint actions are Nash equilibria of the corresponding game. We characterize Nash-rationalizable joint choice behavior by zero-sum games, or games of conflicting interests. If the joint choice behavior forms a product subset, the behavior is called interchangeable. We prove that interchangeability is the only additional empirical condition which distinguishes zero-sum games from general non-cooperative games.     

Core-stem solutions of n-person essential games

A new wide class of internally stable solutions to essential n-person games in characteristic function form, ‘core-stem’ solutions, is herein derived based on the notion of ‘core of a coalition’ and a finite sequence of meta-games (a ‘stem of games’) with a ‘stem-level’ solution for each meta-level. Core-stem solutions exist for every game, can diner according to different stems selected or different stem-level solutions selected. An example with an implausible core and plausible core-stem solution (two different stems) is presented.     

Inefficiency and complementarity in sharing games

A sharing game is a very simple device for partially reconciling an organization’s goal with the interests of its members. Each member chooses an action, bears its cost, and receives a share of the revenue which the members’ actions generate. A (pure-strategy) equilibrium of the game may be inefficient: surplus (revenue minus the sum of costs) may be less than maximal. In a previous paper, we found that for a wide class of reward functions, no one squanders at an inefficient equilibrium (spends more than at an efficient profile) if the revenue function has a complementarity property. In the present paper, we examine the “opposite” of the complementarity property (Substitutes) and we study a class of finite games where squandering equilibria indeed occur if Substitutes holds strongly enough. Squandering equilibria play a key role when one traces the effect of technological improvement on a sharing game’s surplus shortfall. We then turn to the question of choice among reward functions in a principal/agents setting. We find that if we again assume complementarity then strong conclusions can be reached about the reward functions preferred by “society”, by the players (agents), and by the principal.     

What Makes a Blockbuster Video Game? An Empirical Analysis of US Sales Data

This study uses a unique data set of individual video game titles to estimate the effect of an exhaustive set of observable characteristics on the likelihood of a video game becoming a blockbuster title. Due to the long‐tailed distribution of the sales data, both ordinary least squares and logistic regression models are estimated. The results consistently show that blockbuster video games are more likely to be released by one of the major publishers for popular hardware platforms. Results also show that games of higher quality are significantly more likely to sell a greater number of units than those of a lower quality. Copyright © 2013 John Wiley & Sons, Ltd.     

Rationalizability in continuous games

Define a continuous game to be one in which every player's strategy set is a Polish space, and the payoff function of each player is bounded and continuous. We prove that in this class of games the process of sequentially eliminating “never-best-reply” strategies terminates before or at the first uncountable ordinal, and this bound is tight. Also, we examine the connection between this process and common belief of rationality in the universal type space of Mertens and Zamir (1985).     

The Theory of Socially Embedded Games: Applications and Extensions to Open and Closed Games

An earlier article, drawing on the mathematical theory of rules and rule complexes, extends and generalizes game theory (GGT). The theory has been used to conceptualize and analyze diverse social relationships, roles, and games as particular types of rule complexes.For instance, a social role, as a major basis of a parent's action in a game, consists of at least four key components – which are mathematical objects – in the determination of action: value complex, model of reality (including beliefs and knowledge bases), a repertoire of acts, routines, programs, and strategies, and modality, a role-specific algorithm for determining or generating action in game settings. This article applies and extends GGT in analyses of a market bargaining game (a type of open game) and of the classical game of prisoners' dilemma (a type of closed game). The applications show the concrete effects of social embeddedness on game structuring, game interaction patterns and outcomes, and social equilibria.     

The core of the inductive limit of a direct system of economies with a communication structure

This paper studies direct systems of finite, that is with finitely many agents, communication structures, finite (balanced and superadditive) NTU games and finite economies. The inductive limit of such a system is again a communication structure, an NTU game or an economy, this time possibly with infinitely many agents. As a matter of fact, each infinite communication structure, each infinite NTU game and each infinite economy, is the inductive limit of a direct system of finite communication structures, finite NTU games and finite economies. A communication game is an NTU game with a communication structure on the set of players. To each economy, there corresponds a balanced and superadditive NTU game. To each economy with a communication structure on the set of agents, there corresponds a communication game. In the paper it is proved that the core of the inductive limit of a direct system of communication games is not empty and in fact the intersection of the cores of the finite communication games of the direct system. It follows that each infinite economy (with or without a communication structure on the set of agents) has a nonempty core. A direct system of economies is a generalisation of the Debreu and Scarf [Debreu, G., Scarf, H. A limit theorem on the core of an economy, International Economic Review 4, pp. 235–246.] example of `replica economies'. The proof of the nonemptiness of the core of the inductive limit of a direct system of economies is along the lines of the proof by Debreu and Scarf. As by-product it is shown that an NTU game is totally balanced if and only if all its finite subgames are balanced.     

Repeated two-person zero-sum games with unequal discounting and private monitoring

We consider discounted repeated two-person zero-sum games with private monitoring. We show that even when players have different and time-varying discount factors, each player’s payoff is equal to his stage-game minmax payoff in every sequential equilibrium. Furthermore, we show that: (a) in every history on the equilibrium path, the pair formed by each player’s conjecture about his opponent’s action must be a Nash equilibrium of the stage game, and (b) the distribution of action profiles in every period is a correlated equilibrium of the stage game. In the particular case of public strategies in public monitoring games, players must play a Nash equilibrium after any public history.