# N1 - Economics 405/505 Introduction to Game Theory Rui Zhao University at Albany SUNY 1 Strategic Games Theory 1.1 General Idea A strategic game

This preview shows pages 1–2. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Economics 405/505 Introduction to Game Theory Rui Zhao University at Albany, SUNY 1 Strategic Games: Theory 1.1 General Idea A strategic game has three essential components. 1. There is a set of players , 1, ..., i, ..., I. 2. Each player i has a set of strategies S i . 3. Each player i has a payoff function u i : S-→ < , where S = S 1 × ··· × S I . So each player i will receive a payoff u i ( s ) if the strategies chosen by all players turn out to be s = ( s 1 ,...,s I ) . Such a list s is also called a strategy profile . Example 1 Prisoners’ Dilemma. Payoffs Confess Not Confess-5, -5 0, -10 Not-10, 0-1, -1 Example 2 Stag Hunt A group of hunters wish to catch a stag and share it equally. Each hunter can either hunt a stag or a hare, but not both. A stag can be caught only if all hunters devote to hunting stag: it escapes if one hunter tries to hunt a hare. For each hunter, an even share of the stag is better than a hare. Players: the hunters. Strategies: each player has two { Stag, Hare } . Payoffs: Payoffs Stag Hare Stag 2, 2 0, 1 Hare 1, 0 1, 1 1.2 Dominated Strategies Recall that a strategy profile s = ( s 1 ,...,s i ,...,s I ) ∈ S specifies a particular strategy s i for each player i. Denote by s- i = ( s 1 ,...,s i- 1 ,s i +1 ,...,s I ) the profile of strategies of all players other than player i . Set S- i = S 1 ×··· × S i- 1 × S i +1 ×··· S I consists of all such profiles. Thus a strategy profile s can also be written as ( s i ,s- i ), indicating player i ’s strategy being s i and others’ being s- i . Definition 1 A strategy s i is strictly dominated by another strategy s i if u i ( s i ,s- i ) > u i ( s i ,s- i ) for all s- i ∈ S- i . In words, s i is a better strategy than s i for player i , regardless what other players are doing. We also say that strategy s i strictly dominates s i ....
View Full Document

## This note was uploaded on 09/14/2011 for the course ECON 505 taught by Professor Zhao during the Spring '11 term at SUNY Albany.

### Page1 / 4

N1 - Economics 405/505 Introduction to Game Theory Rui Zhao University at Albany SUNY 1 Strategic Games Theory 1.1 General Idea A strategic game

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online