ECS1050.03.post

# ECS1050.03.post - UNIT II The Basic Theory 6/30 Zero-sum...

This preview shows pages 1–9. Sign up to view the full content.

UNIT II: The Basic Theory Zero-sum Games Nonzero-sum Games Nash Equilibrium: Properties and Problems Bargaining Games Bargaining and Negotiation Review Midterm 7/16 6/30

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

View Full Document
Zero-sum Games The Essentials of a Game Extensive Game Matrix Game Dominant Strategies Prudent Strategies Solving the Zero-sum Game The Minimax Theorem
The Essentials of a Game 1. Players : We require at least 2 players (Players choose actions and receive payoffs.) 2. Actions : Player i chooses from a finite set of actions, S = {s 1 ,s 2 ,…. .,s n }. Player j chooses from a finite set of actions T = {t 1 ,t 2 ,……,t m }. 3. Payoffs : We define P i (s,t) as the payoff to player i, if Player i chooses s and player j chooses t. We require that P i (s,t) + P j (s,t) = 0 for all combinations of s and t. 4. Information : What players know (believe) when choosing actions. ZERO-SUM

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

View Full Document
The Essentials of a Game 4. Information : What players know (believe) when choosing actions. Perfect Information : Players know their own payoffs other player(s) payoffs the history of the game, including other(s) current action* *Actions are sequential (e.g., chess, tic-tac-toe). Common Knowledge
Extensive Game Player 1 chooses a = {1, 2 or 3} Player 2 b = {1 or 2} Player 1 c = {1, 2 or 3} Payoffs = a 2 + b 2 + c 2 if /4 leaves remainder of 0 or 1. -(a 2 + b 2 + c 2 ) if /4 leaves remainder of 2 or 3. Player1’s decision nodes -3 -6 -11 -6 9 -14 -6 9 -14 9 12 17 -11 -14 -19 -14 17 -22 GAME 1. “Square the Diagonal” (Rapoport: 48-9) Player 2’s decision nodes 1 3 2 1 2 1 2 3

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

View Full Document
Extensive Game How should the game be played? Solution : a set of “advisable” strategies, one for each player. Strategy : a complete plan of action for every possible decision node of the game, including nodes that could only be reached by a mistake at an earlier node . Player1‘s advisable Strategy in red -3 -6 -11 -6 9 -14 -6 9 -14 9 12 17 -11 -14 -19 -14 17 -22 GAME 1. 1 3 2 1 2 1 2 3 Start at the final decision nodes (in red) Backwards-induction
Extensive Game How should the game be played? Solution : a set of “advisable” strategies, one for each player. Strategy : a complete plan of action for every possible decision node of the game, including nodes that could only be reached by a mistake at an earlier node . Player1‘s advisable Strategy in red -3 -6 -11 -6 9 -14 -6 9 -14 9 12 17 -11 -14 -19 -14 17 -22 GAME 1. Player2’s advisable strategy in green 1 3 2 1 2 1 2 3 Player1’s advisable strategy in red

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

View Full Document
Extensive Game How should the game be played? If both player’s choose their advisable (prudent) strategies, Player1 will start with 2, Player2 will choose 1, then Player1 will choose 2.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 72

ECS1050.03.post - UNIT II The Basic Theory 6/30 Zero-sum...

This preview shows document pages 1 - 9. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online