Complete Information Game Research Articles

On pure-strategy equilibria in games with correlated information

This paper rehabilitates a program initiated in Aumann (1974) by contributing a result to the theory of finite-player Bayesian games in environments that explicitly include correlated information. An equivalence theorem offers conditions under which the set of mixed-strategy equilibrium payoffs in a classical finite-action game of complete information coincides with the set of objective pure-strategy Nash equilibrium (PSNE) expected payoffs in an affiliated Bayesian game with type-independent payoffs. This result is motivated for a non-specialist reader by several examples. An Appendix devoted to an intuitive discussion of the so-called ‘Lebesgue extension’ is added to make the paper self-contained.

On Private Communication in Competing Mechanism Games

We study competing mechanism games in which principals simultaneously design contracts to deal with several agents. We show that principals can profit from privately communicating with agents by generating incomplete information in the continuation game they play. Specifically, we construct an example of a complete information game in which none of the (multiple) equilibria in Yamashita (2010) survives against unilateral deviations to mechanisms involving private communication. This also contrasts with the robustness result established by Han (2007). The role of private communication we document may call for extending the standard construction of Epstein and Peters (1999) to incorporate this additional element.

A note on identification of discrete choice models for bundles and binary games

We study nonparametric identification of single‐agent discrete choice models for bundles (without requiring bundle‐specific prices) and of binary games of complete information. We show that these two models are quite similar from an identification standpoint. Moreover, they are mathematically equivalent when we restrict attention to the class of potential games and impose a specific equilibrium selection mechanism in the data generating process. We provide new identification results for the two related models. Discrete choice demand binary games identification bundles complements substitutes entry games potential games C14 C35 C57 C72

Optimal joint control and triggering strategies against denial of service attacks: a zero‐sum game

This study is concerned with the optimal control and scheduling problem for linear networked control systems with communication constraints and security issues. The communication channel, which connects remote sensors with a controller, has limited transmission capability and may suffer denial of service attacks from an external attacker. Unlike most existing cyber-attack-related literature which presumed a prior well-designed control or estimating strategy on which triggering and jamming strategies were established, in the present work, optimal strategies of the controller, the trigger as well as the external attacker are considered simultaneously under the renowned linear quadratic criteria. A designer, who can jointly devise the controller and the trigger, aims to improve the system's performance while the attacker's goal is just the opposite. With the assumption that the trigger and the attacker have limited opportunities to send or attack, a zero-sum static game of complete information is first utilised to investigate the optimal strategies for both players, i.e. the designer and the attacker. The existence of Nash equilibrium (NE) point, i.e. the combination of optimal strategy for each player, is proven afterwards. Finally, the property of none pure-strategy NE in a special case is provided with rigorous proofs. A numerical example is employed to demonstrate how to derive the optimal strategies for the designer and the attacker.

WEBJET’S COMPETITIVE STRATEGY FROM A GAME THEORY PERSPECTIVE

The Brazilian commercial aviation market has undergone several changes over the past decade with the entry of GOL Airlines (1999) and the exit of firms such as TRANSBRASIL, VARIG and VASP. In 2005, WEBJET obtained a concession for regular public transport, but faced a price war with the traditional companies, coming to suspend its operations less than six months later. Regarding these events, this article aims to show how the reaction of incumbent firms was to the entry of WEBJET into the marketplace, by using Game Theory and the support of the literature on barriers to entry. Through the creation and the resolution of a Dynamic Game of Complete and Imperfect Information, it has been found that WEBJET seems to have underestimated the reaction of the incumbent firms like GOL and TAM, as well as the degree of passengers´ loyalty to the incumbent firms.

Costly Leader Games with a Probabilistically Non-Strategic Leader

I consider a two-person costly leader game — in which the follower endogenously chooses whether to buy information about the leader, and a follow-up action — with a twist. With a known probability, the leader is a nonstrategic type. A strategic type leader may choose to masquerade as a nonstrategic type, at a cost. I show that, if the follower’s cost of information is not too large, and the probability of the leader being nonstrategic is neither too large nor too small, this game has no pure strategy equilibrium. Moreover, the equilibrium of the simultaneous-move complete information game is inaccessible as follower information cost converges to zero. There is no equilibrium outcome in which leader advantage is destroyed: however, a mixed strategy equilibrium exists which does preserve leader advantage in the sense that payoffs and strategies converge to those of the sequential-move complete information equilibrium as information cost tends to zero. My results differ from some traditional results in costly leader games, and are due to the interaction of two forces, the “type uncertainty” and the “money down the drain” effects. To my knowledge this is the first paper to integrate behavioral types into costly leader games (other papers considering heterogeneity in type do not consider nonstrategic players).

On Zermelo's theorem

A famous result in game theory known as Zermelo's theorem says that ''in chess either White can force a win, or Black can force a win, or both sides can force at least a draw. The present paper extends this result to the class of all finite-stage two-player games of complete information with alternating moves. It is shown that in any such game either the first player has a winning strategy, or the second player has a winning strategy, or both have unbeatable strategies.

Extensive Game of Horse Race: A Research on <i>Tian Ji's Horse Race</i> Based on Static Games of Complete Information

There are many ways to develop of the classical problem about Tian Ji's Horse Race so that this problem may be researched deeply using theory of games. Therefore, this paper designs n-order extensive game of horse race by changing a rule of traditional problem. After analysis, this paper holds a belief that this game is a kind of static games of complete information, which means theory of static games of complete information can be used to research Tian Ji's Horse Race . With showing all of the strategy profiles of third-order extensive game of horse race and calculating Nash equilibrium of this game, this paper finds some characteristics of the strategy profiles and Nash equilibrium of extensive game of horse race and give the expression of Nash equilibrium of mixed strategy of this game. A new concept of layout is introduced to reveal how strategy profiles influence the outcome of this game. Then the characteristic of the layouts of extensive game of horse race and the layout that can make Tian Ji’s payoff biggest are found and proved, which is drawn from the result of some simulations about fourth-order and fifth-rank extensive games of horse race using a Java program.

Measuring Drama in Goose-like Games

Abstract For games of complete information with no chance component, like Chess, Go, Hex, and Konane, some parameters have been identified that help us understand what makes a game pleasant to play. One of these goes by the name of drama. Briefly, drama is linked to the possibility of recovering from a seemingly weaker position, if the player is strong enough. This is an important requirement to prevent initial advantages to be amplified into unavoidable and thus uninteresting victories. Drama is a feature that arguably good board games should have, since it is relevant in the perception of the play experience as pleasant. Despite its intrinsic qualitative nature, we suggest the adaptation of the concept of drama to games of pure chance and propose a set of objective criteria to measure it. Some parameters are here used to compare Goose-like games, which we compute via computer simulation for some well-know games. A statistical analysis is performed based on the play of millions of matches done by computer simulation. The article discusses correlations and patterns found among the collected data. The methodology presented herein is general and can be used to compare other types of board games.

Bayesian Estimation of Entry Games with Multiple Players and Multiple Equilibria

Entry game models are often used to study the nature of firms' profits and the nature of competition among firms in empirical studies. However, when there are multiple players in an oligopoly market, the resulting multiple equilibria have made it difficult in previous studies to estimate the payoff functions of players in complete information, static and discrete games without using unreasonable assumptions. To overcome this difficulty, the present paper proposes a practical estimation method for an entry game with three players using a Bayesian approach. Some mild assumptions are imposed on the payoff function, and the average competitive effect is used to capture the entry effect of the number of firms. Our proposed methodology is applied to Japanese airline data from the year 2000, when there were three major airline companies, ANA, JAL and JAS. The model comparison is conducted to investigate the nature of strategic interaction among these Japanese airline companies.

Bayesian Analysis of Entry Games: A Simulated Likelihood Approach Without Simulation Errors

This paper provides a practical guide to Bayesian estimation of simultaneous entry games of complete information with heterogeneous firms. Bayesian inference requires computation of the likelihood, which is carried out by simulating unobservables. To avoid errors from finite simulations, we apply Andrieu and Roberts’s [2009. The pseudo-marginal approach for efficient Monte Carlo computations, Annals of Statistics, 37(2), pp. 697–725] pseudo-marginal approach. We rely also on adaptive Markov chain Monte Carlo algorithms that improve computational performance.

Bargaining in the shadow of a commitment problem

This paper reports results from laboratory experiments on how commitment problems affect bargaining choices. Subjects are randomly assigned the conditions that produce a commitment problem in order to estimate the effect the commitment problem condition has on bargaining behavior. The empirical results suggest subjects are consistently responsive to the commitment problem condition. When presented with a commitment problem, most subjects identify the condition and choose the present day lottery over future negotiation. Moreover, subjects not exposed to the commitment problem condition bargain as if they were playing the one-stage ultimatum game. Subjects in both games are responsive to their own costs rather than their opponents, playing as if this complete information game were in an incomplete information setting.

On noncooperative oligopoly equilibrium in the multiple leader–follower game

In this paper, we provide new proofs of existence and uniqueness of a Stackelberg market equilibrium for a multiple leader–follower noncooperative oligopoly model in which heterogeneous firms compete on quantities. To this end, we consider a two-stage game of complete and perfect information in which many leaders interact strategically with many followers. The Stackelberg market equilibrium constitutes a pure strategy subgame perfect Nash equilibrium of this game. Existence and uniqueness are more difficult to handle in this framework, insofar as the presence of several leaders and followers displays a richer set of strategic interactions. Then, to prove existence, we notably provide a new procedure to determine (the conditions under which) the optimal behavior of the followers (may be written) as functions of the sole strategy profile of the leaders. Some examples outline our procedure and discuss our assumptions.

A Framework of Camera Source Identification Bayesian Game.

Image forensics with the presence of an adversary, such as the interplay between the sensor-based camera source identification (CSI) and the fingerprint-copy attack, has attracted increasing attention recently. In this paper, we propose a framework of CSI game with both complete information and incomplete information. A noise level-based counter anti-forensic method is presented to detect the potential fingerprint-copy attack, and unlike the state-of-the-art countermeasure of the triangle test, it does not need to collect the candidate image set. With the existence of countermeasure, a rational forger needs to balance the tradeoff between synthesizing source information and leaving new detectable evidence of raising the noise level of a forged image. The mixed-strategy other than the sequential-move assumption is adopted to solve the games. The Bayesian game is introduced to address the information asymmetry in practice. The Nash equilibrium of both the complete information game and Bayesian game are theoretically analyzed, and the expected Nash equilibrium payoff of a Bayesian game is obtained. Nash equilibrium receiver operating characteristic curves are adopted to evaluate the detection performance. Simulation results show that the information asymmetry can remarkably affect the final detection performance. To our knowledge, this paper is the first attempt in analyzing a Bayesian forensic game with practical information asymmetry.

Strategic maritime container service design in oligopolistic markets

This paper considers the maritime container assignment problem in a market setting with two competing firms. Given a series of known, exogenous demands for service between pairs of ports, each company is free to design liner services connecting a subset of the ports and demand, subject to the size of their fleets and the potential for profit. The model is designed as a three-stage complete information game: in the first stage, the firms simultaneously invest in their fleet; in the second stage, they individually design their services and solve the route assignment problem with respect to the transport demand they expect to serve, given the fleet determined in the first stage; in the final stage, the firms compete in terms of freight rates on each origin–destination movement. The game is solved by backward induction. Numerical solutions are provided to characterize the equilibria of the game.

Endogenous information acquisition in Bayesian games with strategic complementarities

This paper studies covert (or hidden) information acquisition in common value Bayesian games of strategic complementarities. Using the supermodular stochastic order to arrange the structures of information increasingly in terms of preferences, we provide novel, easily interpretable and verifiable, though restrictive conditions under which the value of information is increasing and convex, and study the implications in terms of the equilibrium configuration. Increasing marginal returns to information leads to extreme behavior in that agents opt either for the highest or the lowest quality signal, so that the final analysis of this complex game simplifies greatly into that of a two-action game. This result can rationalize the complete information game as an endogenous outcome. Finally, we also establish that higher-quality information leads players to select more dispersed actions in the Bayesian game.

Dynamic commitment games, efficiency and coordination

An important form of commitment is the ability to restrict the set of future actions from which choices can be made. We study a simple two player dynamic game of complete information which incorporates this type of commitment. For a given initial game, the players engage in an endogenously determined number of commitment periods before choosing from the remaining actions. We show the existence of equilibria with pure strategies in the commitment periods. Partial characterization results for general games capture the tradeoff between commitment and deterrence. The equilibrium outcome is unique and efficient for two classes of games, including pure coordination and stag-hunt games.

The empirical content of games with bounded regressors

This paper develops a strategy for identification and estimation of complete information games that does not require a regressor that has large support or a parametric specification for the distribution of the unobservables. The identification result uses a nonstandard but plausible condition on the unobservables: the assumption that the joint density of the unobservables of all agents is unimodal in the sense of achieving the global maximum at a unique point. Also, a three-step semiparametric estimator is proposed. Under mild regularity conditions, the estimator is consistent and asymptotically normally distributed. The estimator is nonstandard in the sense that the estimators of the intercept and interaction effect parameters converge at slower than the parametric rate. An intermediate result concerns identification and estimation of the direction of the interaction effect.

Bayesian Nash equilibrium and variational inequalities

This paper provides a sufficient condition for the existence and uniqueness of a Bayesian Nash equilibrium by regarding it as a solution of a variational inequality. The payoff gradient of a game is defined as a vector whose component is a partial derivative of each player’s payoff function with respect to the player’s own action. If the Jacobian matrix of the payoff gradient is negative definite for each state, then a Bayesian Nash equilibrium is unique. This result unifies and generalizes the uniqueness of an equilibrium in a complete information game by Rosen (1965) and that in a team by Radner (1962). In a Bayesian game played on a network, the Jacobian matrix of the payoff gradient coincides with the weighted adjacency matrix of the underlying graph.

An Ordinal Game Theory Approach to the Analysis and Selection of Partners in Public–Private Partnership Projects

Nowadays, public---private partnership projects have become a standard for delivering public services in both developed and developing countries. In this paper, we are concerned with the analysis of private sector proposals and the selection of the private sector partner to whom to award the contract. To the best of our knowledge, this problem has not been addressed within a game theory framework. To fill this gap, we model this decision problem as a static non-cooperative game of complete information and propose a new ordinal game theory algorithm for finding an optimal generalized Nash equilibrium. The proposed algorithm determines a single ranking of proposals or bidders that takes account of multiple performance criteria and reflects both the public sector and the private sector perspectives, and can handle any number of private sector players and any number of contractual terms. An illustrative scenario is provided to guide the reader through the workings of the proposed ordinal game theory algorithm. The proposed ordinal game theory-based analysis framework can be used by the private sector to analyse any set of potential proposals most likely to be submitted by bidders and to assist with the choice of bidding strategies, and by the public sector player to analyse any set of potential proposals most likely to be submitted under any set of contractual terms and to assist with the choice of a realistic set of contractual terms and their performance measures.