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Graduate School of Economics Waseda University Waseda University
Graduate School of Economics Waseda University Waseda University

... the game. Furthermore, it is known that the maximization of a potential function derives the robust equilibrium, provided that the equilibrium is unique (Ui, 2001). In addition, the existence of a potential function ensures the “Fictitious Play Property,” ensuring the convergence of one-side better ...
XX On the Complexity of Approximating a Nash Equilibrium
XX On the Complexity of Approximating a Nash Equilibrium

... more appropriate. If instead the incentive to switch is perceived to be as strong in the two situations, then the additive notion of approximation is more fitting. From a computational complexity standpoint, additive and relative approximations have thus far enjoyed similar fate. In two-player games ...
Multi-player approximate Nash equilibria
Multi-player approximate Nash equilibria

... The problem of computing of a Nash equilibrium is one of the most fundamental problems in modern game theory. Given the evidence of its intractability, in recent years an extensive research has focused on the approximation of Nash equilibria. In this paper we study the fundamental problem of the com ...
Models and Games
Models and Games

... proofs and constructions but it is also important to know how to make the intuitive arguments and concepts mathematically exact. ...
Coordination Mechanisms∗
Coordination Mechanisms∗

... Mechanisms to improve coordination of selfish agents is not a new idea and we only mention here work that directly relates to our approach. A central topic in game theory [32] is the notion of mechanism design2 in which the players are paid (or penalized) to “coordinate”. Another attempt is the intr ...
Chapter 6 Games - Cornell Computer Science
Chapter 6 Games - Cornell Computer Science

... Underlying Assumptions. In order to make this question tractable, we will make a few assumptions. First, we assume everything that a player cares about is summarized in the player’s payoffs. In the Exam-or-Presentation Game described in Section 6.1, this means that the two players are solely concern ...
Defining Winning Strategies in Fixed-Point Logic
Defining Winning Strategies in Fixed-Point Logic

... are used to model reactive systems where the construction of winning strategies corresponds to the synthesis of controllers. Strategies can be viewed and presented in several different ways, and it is not always obvious what definability of strategies really means. However, for the games that we cons ...
Imperfect Best-Response Mechanisms
Imperfect Best-Response Mechanisms

... Related work. Convergence of best-response dynamics is a main topic in game theory. It relates to the so-called problem of equilibrium selection, that is, how the players converge to an equilibrium (see the book by Harsanyi and Selten [13]). Noisy versions of best-response dynamics have been studied ...
Language-based Games - Cornell Computer Science
Language-based Games - Cornell Computer Science

... where a type of procrastination is represented by a minor extension of the underlying language. We make three major contributions. First, as noted, our system is easy to use in the sense that players’ preferences are represented with a simple and uncluttered formalism; complex psychological phenomen ...
Toward the fair sharing of profit in a supply network formation
Toward the fair sharing of profit in a supply network formation

... concepts have been introduced for approaching the stability issue. A necessary condition for the stability of a coalition is that no set of players is able to increase its members’ profits by forming a different coalition. The set of payoff profiles that verifies this property is known as the core o ...
Extensive Form Correlated Equilibrium: Definition and
Extensive Form Correlated Equilibrium: Definition and

... of move combinations at parallel information sets may grow exponentially, and each of them may produce a different conditional distribution for the recommended move. This applies in general for CE, with possibly exponentially many recommended strategies and corresponding conditional distributions. T ...
On Oblivious PTAS`s for Nash Equilibrium
On Oblivious PTAS`s for Nash Equilibrium

... either zero or Ω(1) — and thus with support of bounded size — then obviously this equilibrium can be found exhaustively in polynomial time. Somewhat surprisingly, we show that there is a PTAS for the class of games whose equilibria are guaranteed to have small — O( n1 ) — values, and therefore large ...
Strategic Behavior in Non-Atomic Games
Strategic Behavior in Non-Atomic Games

... Modeling economic situations featuring a large number of agents with non-atomic games is especially convenient because the inability of players to affect societal variables provides significant technical ease. However, this advantageous feature may result in the dismissal of the strategic behavior d ...
e-Consistent equilibrium in repeated games - IMJ-PRG
e-Consistent equilibrium in repeated games - IMJ-PRG

... stage of the game, are e-rational. That is, players are consistent: they take into consideration the future normalized payo¨s they face and use e-optimizing strategies at every period. This de®nition di¨ers from the traditional de®nition in that in the latter there may exist events where players are ...
Document
Document

... Mixed strategy Nash equilibrium I A mixed strategy for a player in a strategic game is a probability distribution over his/her available actions. ...
The Least Square Nucleolus is a Normalized Banzhaf Value
The Least Square Nucleolus is a Normalized Banzhaf Value

... According to the Banzhaf value, we observe that there are two weak (but not symmetric) players, 1 and 2, and three strong players, 3, 4, and 5. In this case, the additive normalization of the Banzhaf value proposes a payoff below the first agent’s standalone worth. Consequently, Bt differs from Ba . ...
The Complexity of Partial-observation Stochastic Parity Games With
The Complexity of Partial-observation Stochastic Parity Games With

... The class of ω-regular objectives. An objective specifies the desired set of behaviors (or paths) for player 1. In verification and control of stochastic systems an objective is typically an ω-regular set of paths. The class of ω-regular languages extends classical regular languages to infinite str ...
Evolutionary Game Theory: The Game of Life
Evolutionary Game Theory: The Game of Life

... competition for these resources. Darwin also realized that within any group of similar organisms there are variations, and certain variations may result in some organisms being better competitors for limited resources. The individuals least successful at getting resources will fail to obtain those n ...
Adversarial search --- Games / Deep Blue (auxiliary materials)
Adversarial search --- Games / Deep Blue (auxiliary materials)

... – Chess 4.x, first to play at Master's level – trades a little time for a huge reduction in space • lets you do breadth-first search with (more space efficient) depthfirst search ...
The Dice Game
The Dice Game

... a sort of dice-based fruit machine. You could imagine that it will be used in experiments on gambling in some Psychology research. I want to have a number of dice, initially 3 but it is nice to make this flexible, which the player can choose to roll individually or all together. The player’s goal is ...
Computing the Optimal Strategy to Commit to
Computing the Optimal Strategy to Commit to

... problem is that there may be multiple Nash equilibria. This leads to the equilibrium selection problem of how an agent can know which strategy to play if it does not know which equilibrium is to be played. When the setting is modeled as an extensive-form game, it is possible to specify that some pla ...
Team-Maxmin Equilibria
Team-Maxmin Equilibria

... Many interactions involve teams of participants that have coinciding interests but must act individually. For example, the individuals in a company work toward a common goal, but often must make their decisions independently. Coordinating their actions may be impossible or too expensive. Similarly, ...
Multiplicative updates outperform generic no-regret learning in congestion games
Multiplicative updates outperform generic no-regret learning in congestion games

... Roughgarden [31]. Analyzing the inefficiency of Nash equilibria provides useful information about the solution quality achieved by selfish players once they reach an equilibrium, but does not provide a model of how selfish players behave, and it says little about whether selfish players will coordin ...
Playing Large Games using Simple Strategies
Playing Large Games using Simple Strategies

... Non-cooperative game theory has been extensively used to analyze situations of strategic interactions. Recently, it has been pointed out [24, 14, 27] that many internet related problems can be studied within the framework of this theory. The most important solution concept in non-cooperative games i ...
TIME AVERAGE REPLICATOR AND BEST REPLY
TIME AVERAGE REPLICATOR AND BEST REPLY

... approximation at Xt with error rate 1t . 2. Unilateral processes The model will be in the framework of an N -person game but we consider the dynamics for one player, without hypotheses on the behavior of the others. Hence, from the point of view of this player, he is facing a (measurable) vector out ...
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Game mechanics

Game mechanics are constructs of rules or methods designed for interaction with the game state, thus providing gameplay. All games use mechanics; however, theories and styles differ as to their ultimate importance to the game. In general, the process and study of game design, or ludology, are efforts to come up with game mechanics that allow for people playing a game to have an engaging, but not necessarily fun, experience.The interaction of various game mechanics in a game determines the complexity and level of player interaction in the game, and in conjunction with the game's environment and resources determine game balance. Some forms of game mechanics have been used in games for centuries, while others are relatively new, having been invented within the past decade.Complexity in game mechanics should not be confused with depth or even realism. Go is perhaps one of the simplest of all games, yet exhibits extraordinary depth of play. Most computer or video games feature mechanics that are technically complex (in terms of making a human do all the calculations involved) even in relatively simple designs.In general, commercial video games have gone from simple designs (such as Space Invaders and Asteroids) to extremely complex ones (such as Gran Turismo 5 and Crysis 2) as processing power has increased. In contrast, casual games have generally featured a return to simple, puzzle-like designs, though some are getting more complex. In physical games, differences generally come down to style, and are somewhat determined by intended market.
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