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Strategic Decision Making in Game Theory: Nash Equilibrium Explained

Learn about Nash Equilibrium, Best Response Strategies, and Partnership Games in game theory through a detailed review of Yale lectures. Understand how iterative deletion of dominated strategies can lead to optimal outcomes. Explore the concept of Mutual Best Response and delve into the calculations involving effort levels and profit sharing. Gain insights into finding the optimal strategies in a game scenario and recognizing Nash Equilibrium. Dive deep into the realm of strategic thinking and decision-making in game theory.

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Strategic Decision Making in Game Theory: Nash Equilibrium Explained

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  1. Yale lectures 3 and 4 review • Iterative deletion of dominated strategies. • Ex: two players choose positions on political spectrum. Endpoints become repeatedly eliminated by deletion of dominated strategies.

  2. Median Voter Theorem

  3. Median Voter Theorem

  4. Median Voter Theorem

  5. Median Voter Theorem

  6. Best ResponseNo dominated strategies

  7. In this case… • Each of player 1’s actions is a best response to some mixed strategy of player 2. • If you have an action that is never a best response, don’t play it. • The best response is the strategy (or strategies) which produces the most favorable outcome for a player, taking other players' strategies as given.

  8. Finding a mutual best response Partnership game b is synergy. s1 and s2 are effort levels. Max s1 2(s1 + s2 +bs1s2) –(s1)2 Use calculus – differentiate and set to zero 2(1+bs2) –2(s1) = 0 1+bs2 =(s1) Best response function for s1 1+bs1 =(s2) Best response function for s2 if equal (as symmetric), 1+b(1+bs1) =(s1) s1 = 1/(1-b) Your share of the profit Your cost of effort

  9. Mutual Best response graph if b=1/4

  10. Nash Equilibrium • If we are at a Nash Equilibrium, neither player has an incentive to deviate.

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