Intelligent Game Theory

Introduction to the course

• Introduction to Game Theory

− Zero-sum games: pure and mixed strategies

− Non-zero-sum games: Nash equilibrium

− Strategic moves: cooperation and threats

− Arbitration schemes

− N-player games: Shapley value

− Algorithms for solving game matrices

• Improvements to Alpha-Betas

− MTD family of game tree search algorithm

• Human vs. Machines: styles of play

• New techniques in automatic Game-Playing

− Memory-Based/Case-based paradigms

− Automatic learning of Game Strategies

• Games of Strategy

• Adaptive Behaviour

• Distributed Games

• Famous systems, and how they work.

Introduction to Game Theory

Game theory is the analysis (mathematical or otherwise)

of situations which involve conflict and/or cooperation.

A game is characterised by:

1. Two or more players. These players can be any

entity such as a person, a company, a nation, the

natural world and even chance.

2. Each player has a number of strategies (possibly

infinite). A strategy represents a course of actions

the player may choose to follow throughout the

game.

3. The outcome of the game is solely determined by

each players choice of strategies.

4. Each outcome is associated with a set of numerical

payoffs, one for each player. These payoffs

represent the “value” of the outcome of the game to

each player.

An important assumption in game theory is that the

players behave rationally. The goal of each player is to

maximise the payoff the player will receive. The player

has some influence on the outcome of a game since the

player selects their own strategy. But it is the

combination of the strategies selected by each player that

determines the outcome. Sometimes the will be conflict

among the players, such that if player A chooses strategy

X to maximise their payoff then the other players will

lose or gain very little. On other occasions there will be

opportunities for cooperation, where some or all of the

players can work together (by agreement or plausible

threat) to achieve a better payoff than would be possible

if they played individually.

Game theory is not the total solution. Why not?

1. Games in the real world (economic, social,

strategic,...) are very complex and it is unlikely that

you can enumerate all the possible strategies and

accurately evaluate all the possible outcome and

payoffs. However simplified models can realise

simplified versions of the real world game that may

provide an insight into the real world.

2. Game theory presumes rational behaviour by the

players. How many people appear to behave

rationally to you? Do you appear rational to them?

Are your perceptions of the value of the various

payoffs an accurate reflection of their perceived

value of the same payoffs?

3. When you have more than two players or when the

interests of each player are not completely opposed

game theory does not give a unique solution to the

game. What it does offer is a set of suggestions and

partial prescriptions.