Search results
This chapter defines the concept of subgame-perfect equilibrium and illustrates how one can check whether a strategy profile is a subgame perfect equilibrium. 11.1 Definition and Examples. An extensive-form game can contain a part that could be considered a smaller game in
A subgame perfect Nash equilibrium (SPNE) is a strategy profile that induces a Nash equilibrium on every subgame • Since the whole game is always a subgame, every SPNE is a Nash equilibrium, we thus say that SPNE is a refinement of Nash equilibrium • Simultaneous move games have no proper subgames and thus every Nash equilibrium is ...
The equilibrium outcome of the above Nash equilibrium above is that rm 1 sets the price and rm 2 sets the price (A )=2. If rm 1 were to hypothetically choose q1 > 0, then rm 2 would obtain negative pro ts if it indeed follows through with q 2(q1). q2(q1) = 0 since producing at all gives negative pro ts.
If s is a dominant strategy equilibrium, then s is a Nash equilibrium. Proof: Let s be a dominant strategy equilibrium. Take any player i. Since s i is a dominant strategy for i, for any given s i, u i(s i;s i) u i(s i;s i);8s i 2S i. In particular, u i(s i;s i) u i(s i;s i) Since i and s i are arbitrary, this shows that s is a Nash equilibrium.
subgame-perfect Nash equilibrium is a Nash equilibrium whose sub strategy profile is a Nash equilibrium at each subgame. game, ... ... the set of subgame-perfect equilibria is the set of strategy profiles that are computed via backward induction. A subgame-perfect equilibrium? T = {l,2, ... , n-l,n, ... } If t is odd,
Nash equilibrium Given: N-player game A vector s = (s 1, …, s N) is a (pure strategy) Nash equilibrium if: s i ∈R i(s-i) for all players i. Each individual plays a best response to the others.
The definition above covers only the pure strategies. We can define the Nash equilibrium for mixed strategies by changing the pure strategies with the mixed strategies. Again given the mixed strategy of the others, each agent maximizes his expected payoff over his own (mixed) strategies.
