Petrosyan Leon A - Game Theoretic Analysis

David W. K. Yeung

Hong Kong Shue Yan University, Hong Kong & Saint Petersburg State University, Russia

Leon A. Petrosyan

Saint Petersburg State University, Russia

Strategic behavior in the human and social world has been increasingly recognized in theory and practice. From a decision-makers perspective, it becomes important to consider and accommodate the interdependencies and interactions of human decisions. As a result, game theory has emerged as a fundamental instrument in pure and applied research.

In game theory, a non-cooperative game is a game with competition between individual players and in which only self-enforcing are possible due to the absence of external means to enforce cooperative behavior as opposed to cooperative games. In fact, non-cooperative games are the foundation for the development of cooperative games by acting as the status quo. Non-cooperative games are generally analysed through the framework of equilibrium, which tries to predict players individual strategies and payoffs. Indeed, equilibrium analysis is the centre of non-cooperative games. is on non-cooperative games and equilibrium analysis and it contains a variety of recently developed non-cooperative games and non-cooperative game equilibria.

It is well known that non-cooperative behaviours, in general, would not lead to a Pareto optimal outcome. Highly undesirable outcomes (like that in the prisoners dilemma) and devastating results (like the tragedy of the commons) could appear when the involved parties only care about their individual interests in a non-cooperative situation. Cooperative games offer the possibility of obtaining socially optimal and group efficient solutions to decision problems involving strategic actions. In addition, axiomatic values serve as guidance for establishing cooperative solutions. presents a collection of recent cooperative games and axiomatic values.

. These chapters include state-of-art non-cooperative games and original game equilibrium concepts are provided.

In , Jane M. Binner, Francesco Ciardiello, Leslie R. Fletcher and Vassili N. Kolokoltsov analyze strict Nash equilibria in a duopolistic market share model. They developed an advertising model where generic and brand advertising marketing effects are combined in a duopolistic market with inelastic demand, linear advertising costs and strictly positive discount factors. The nontrivial existence of investment Nash equilibrium in pure strategies is derived and the absence of cheap or free riding equilibria is proved. The relationship between predatory and generic marketing effects and the optimal timing of investments and other marketing scenarios are examined.

In , Atsuhiro Satoh and Yasuhito Tanaka examine maximin and minimax strategies in two-players game with two strategic variables, x and p. Two patterns of game one is the x-game in which the strategic variables of players are xs, and the other is the p-game in which the strategic variables of players are ps are considered. It is shown that the maximin strategy and the minimax strategy in the x-game, and the maximin strategy and the minimax strategy in the p-game are all equivalent for each player.

In , Sebastien Rouillon considers a non-cooperative dynamic contribution game in which a group of agents collaborates to complete a public project. The agents exert efforts over time and get rewarded upon completion of the project, once the cumulative effort has reached a pre-specified level. We explicitly derive the cooperative solution and a noncooperative Markov-perfect Nash equilibrium. The author characterizes the set of socially efficient projects, i.e., projects that cooperative groups find worth completing. Comparing with the Markov-perfect Nash equilibrium, it is found that noncooperative groups give up large socially efficient projects and take longer to complete the projects.

In , David Yeung and Ovanes Petrosian formulate a new approach to analyze infinite horizon dynamic games with uncertainties and unknowns in the players future payoff structures. Many events in the considerably far future are intrinsically unknown. Information about the players future payoffs will be revealed as the game proceeds. Making use of the newly obtained information, the players revise their strategies accordingly, and the process will continue indefinitely. This new approach for the analysis of infinite horizon dynamic games via information updating provides a practical alternative to the study of infinite horizon dynamic games.

In of a supply chain consisting of a manufacturer and a single retailer is constructed. The manufacturer sets a production rate and the rate of advertising efforts while the retailer chooses a purchase rate and the consumer price. The state of the game is summarized in the firms backlogs and the manufacturers advertising goodwill. Depending on whether the supply chain members have and share state information, they may either make decisions contingent on the current state of the game (feedback Nash strategy), or precommit to a plan of action during the whole game (open-loop Nash strategy). Given a contract type, the impact of the availability of information regarding the state of the game on the firms decisions and payoffs is investigated.

In , Vladimir Mazalov and Anna Melnik consider a non-cooperative transport game of n players on a communication graph. Here players are passenger transportation companies (carriers). Service requests form a Poisson process with an intensity rate matrix . Players announce prices for their services and passengers choose an appropriate service by minimizing their individual costs (the ticket price and the expected service time). For each carrier, the authors solve the pricing problem and define the equilibrium intensity flows in the conditions of competition.

In , Koji Okuguchi and Takeshi Yamazaki study the existence of unique equilibrium in Cournot mixed oligopoly. They consider the properties of Cournot mixed oligopoly consisting of one public firm and one or more than one private firms. After proving the existence of a unique equilibrium in Cournot mixed oligopoly under general conditions on the market demand and each firms cost function, the authors derive conditions ensuring the existence of a unique Nash equilibrium for the mixed oligopoly where one public firm and at least one of the private firms are active in a general model of Cournot mixed oligopoly with one public firm and several private firms.

In , Gisle Umbhauer studies second-price all-pay auctions and best-reply matching equilibria. The chapter considers second-price all-pay auctions wars of attrition in a new way, based on classroom experiments and best-reply matching equilibrium. The behavior probability distributions in the classroom experiments are strikingly different from the mixed Nash equilibrium. They fit with best-reply matching and generalized best-reply matching. The analysis goes into the generalized best-reply matching logic, highlights the role of focal values and discusses the high or low payoffs this logic can lead to.

In , Pierre von Mouche and Takashi Sato discuss the issue of Cournot equilibrium uniqueness at 0 discontinuous industry revenue and decreasing price flexibility. They consider the equilibrium uniqueness problem for a large class of Cournot oligopolies with convex cost functions and proper price function with decreasing price flexibility. They also illustrate the Selten-Szidarovszky technique based on virtual backward reply correspondences. An algorithm for the calculation of the unique equilibrium is provided.

In normal-form game to a canonical extension, which allows each player to adjust his or her move with a certain probability. The commitment measure relates to the average over all adjustment probabilities for which the given Nash equilibrium can be implemented as a subgame-perfect equilibrium in the canonical extension.