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GAME THEORY. LEARNING GUIDE.

3D MODULE: DOMINANT STRATEGIES. We had already mentioned the key elements for any game:  The players.  The strategies.  The payoffs. Now we explain more deeply somenecessary concepts for the theory, like a “Normal” game, “Common Knowledge”, and we explain a first solution method, called “Strictly dominant strategies”. We show some examples of a standard game,and we see how does this first solution method work. Any solution method for a game, tries to predict players’ behavior and decisions. EXPECTED OUTCOMES. By the end of this module, the student must beable to:  Depict a game matrix.  Identify if a game has (strictly) dominant strategies.  Find a solution for such kind of game. SECOND SESSION ACTIVITIES: 1. Read GIBBONS’ Book first chapter.(Section 1.1). (25 minutes). 2. Read Second module presentation. (20 minutes). 3. Solve the Homework (15 minutes). HOMEWORK: Design, formulate and solve 3 different static games. You must: 1. 2. 3. Showthe preferences order associated over strategy profiles. Explain why the preferences order is such like that. Build the payoffs matrix based upon such preferences.

UNIVERSIDAD DEL ROSARIO GAMETHEORY. LEARNING GUIDE.

4.

Find a Dominant – Strategy solution for the proposed Game.

Example: Two students must solve a homework together. The available strategies for each one of them, are Towork or NOT to work about it. Thus, the preferences order over the strategy profiles, are: (N, W): I won't work, the other student works. (W, W): If I work, the other student must work. (W, N): I work,the other student doesn't. (N, N): None of us work, so we get a zero. This preferences order will keep for any one of the two players. So I assign payoffs which satisfy these preferences. Then: ui(N,W) = 4, ui(W, W) = 3 ui(W, N) = 2 ui(N, N) = -1. Then, the payoffs matrix is: STUDENT 2 WORK STUDENT 1 WORK NOT TO WORK 3, 3 4, 2 NOT TO WORK 2, 4 -1, -1

This game, doesn't have a Dominant...