03.SimultaneousMove1

03.SimultaneousMove1 - SIMULTANEOUS-MOVE GAMES (Also...

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Unformatted text preview: SIMULTANEOUS-MOVE GAMES (Also called: ONE-SHOT GAMES) A SIMULTANEOUS-MOVE GAME IS A GAME IN WHICH PLAYERS CHOOSE THEIR STRATEGIES ONCE, WITHOUT KNOWLEDGE OF EACH OTHERS STRATEGIES. .. THEREFORE NO PLAYER ACTUALLY OBSERVES OTHER PLAYER(S) ACTIONS BEFORE MAKING HIS/HER DECISION. SIMULTANEOUS-MOVE GAMES ARE IMPERFECT INFORMATION GAMES. SIMULTANEOUS-MOVE GAMES FIT WELL TO SITUATIONS IN WHICH PLAYERS (i) ACT ONCE AND AT THE SAME TIME ; (ii) MAY BE ACTING IN DIFFERENT TIMES BUT (DUE TO A LACK OF COMMUNICATION) CANNOT KNOW EACH OTHERS ACTIONS . WE FIRST LOOK AT SIMULTANEOUS-MOVE GAMES WITH FINITE NUMBER OF STRATEGIES FOR EACH PLAYER: THE STRATEGY SET HAS A FINITE NUMBER OF ALTERNATIVES. PLAYER i strategy set is S i = { s i1 , s i2 , , s iN } 1 WE DEFINE: Strategy : A complete contingent plan of action : Action : A particular choice available when the player moves. WE WILL SEE THAT IN DYNAMIC GAMES OF COMPLETE INFORMATION, STRATEGY AND ACTION ARE NOT IDENTICAL NOTIONS. IN SIMULTANEOUS-MOVE GAMES, STRATEGY AND ACTION BECOME EQUIVALENT NOTIONS. MATHEMATICALLY, A SIMULTANEOUS-MOVE GAME CONSISTS OF: A SET OF PLAYERS A STRATEGY (ACTION) SET FOR EACH PLAYER AN OUTCOME, and A PAYOFF CONFIGURATION at each outcome. SIMULTANEOUS-MOVE GAMES ARE OFTEN REPRESENTED BY A GAME MATRIX, CALLED THE STRATEGIC FORM (OR THE NORMAL FORM ). GIVEN A TEXT DESCRIBING A SIMULTANEOUS-MOVE GAME (with two players), STUDENTS CHECKLIST (to form the game matrix): 1. Identify the players, determine who is choosing columns, who is choosing rows 2. Identify each players strategies (hence, actions) as rows or columns; 3. Identify the payoffs to each player resulting from each combination of strategies. If there are random events that affect the payoffs after the players chose their strategies, the payoff of each player is calculated in expected terms. 4. Complete the game matrix, putting the payoffs in their appropriate cells. 5. Try solving the game by applying a solution (Equilibrium) concept. 2 REPRESENTING THE GAME CORRESPONDING TO A TEXTUAL DESCRIPTION AN EXAMPLE: TWO CYCLISTS ON THE ROAD Two cyclists, Arif and Mrs Boutenko, are driving from opposite directions. They suddenly came face to face and had to make a choice, immediately. If both choose left, or if both choose right, they can avoid crashing into each other. But if one of them chooses left while the other chooses right, they will inevitably crash to each other. A crash outcome yields each player the payoff 5. If there is no crash, each player gets 0. Lets assume Boutenko is the player who chooses rows (Player 1). So, Arif will be player 2, choosing one of the columns....
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This note was uploaded on 03/16/2012 for the course FENS 101 taught by Professor Selçukerdem during the Fall '12 term at Sabancı University.

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03.SimultaneousMove1 - SIMULTANEOUS-MOVE GAMES (Also...

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