Αποτελέσματα Αναζήτησης
23 Ιουλ 2002 · 1, 1 2, 1 2, 2. Figure 46.2 The game in Exercise 46.1. EXERCISE 46.2 (Nash equilibrium and weakly dominated actions) Give an exam-ple of a two-player strategic game in which each player has nitely many actions and in the only Nash equilibrium both players' actions are weakly dominated.
Exercise 37.1 (Finding Nash equilibria using best response functions) 10 Exercise 38.1 ( Constructing best response functions ) 11 Exercise 38.2 ( Dividing money ) 11
Even though there is no equilibrium in dominant strategies (because none of the players has a dominant strategy) it turns out that there are at least two Nash-equilibria: (H, H) and (B, B). It is very easy to verify that these are both Nash-equilibria: (HH) is a Nash equilibrium because.
I The symmetric Nash equilibrium is given by q = a c b(N + 1) I Thus XN j=1 qj = N (a c) b(N + 1) p = a N a c (N + 1) <a j = (a c)2 b(N + 1)2
In this game, ( ) is a dominant strategy equilibrium, but ( ) is also a Nash equilib-rium. This example also illustrates that a Nash equilibrium can be in weakly dominated strategies. In that case, one can rule out some Nash equilibria by eliminating weakly dominated strategies.
• In the last lecture, we learned about Nash equilibrium: what it means and how to solve for it • We focused on equilibrium in pure strategies, meaning actions were mapped to certain outcomes • We will now consider mixed strategies: probabilistic play • But first, we have to develop a notion of preferences over
Nash equilibrium. Let s be a strong Nash equilibrium such that u(s) is Pareto optimal in V(N). If u(s) is not in the core of (N;V ), then there is a coalition S , N and a payo vector (u0 i) i2S 2V (S) such that u0 i >u i(s) for all i 2S. Using the definition of V , we get that for every NnS-strategy s0 NnS, in particular for the NnS-strategy s
