- The expected payoff of player 1 from the mixed strategy is the __________ of the expected payoff for each of her _________strategies, where the weights are the probabilities given by _____.
|B.||weighted average; dominant; player 2|
|C.||weighted sum; pure;|
|D.||weighted difference; mixed; nature|
- Consider a two-person game, where player 1 has two strategies and player 2 has three strategies. Which of the following express a mixed strategy equilibrium? [mark all that apply]
|A.||where is the probability distribution of player 1 over her pure strategies, similar for .|
|C.||[(p, 1-p,0), (q, 1-q)] and p and q are in the interval [0,1]|
|D.||[S1, S2] where S1 and S2 are the sets of pure strategies of player 1 and 2.|
|E.||[(p1, p2,1-p1-p2), (1, 0)] and p1 and p2 are in the interval [0,1]|
- Whenever we add uncertainty to a game and a player would like to outguess the others, ________ a NE in _________ strategies. Players would assign ________ to the its strategies in Si, and this gives us the notion of ___________ strategies.
|A.||There is not; mixed; values; dominated|
|B.||There is; weak; maximin values; maximin|
|C.||There is not; pure; weights; dominant|
|D.||There is ; pure ;probabilities; mixed|
- Mark the correct sequence for the following statements:
- Finite games have at least one Nash equilibrium in pure strategies.
- A pure strategy may be strictly dominated by a mixed strategy, even if this pure strategy is not strictly dominated by any other pure strategy.
III. A pure strategy can be a best response for a mixed strategy if and only if such pure strategy is also best response to any other pure strategy.
- Consider a kicker (K) and a goalie (G) in a soccer game. Suppose that if K kicks to the right and G jumps to the right, the probability of a goal is 0.3. If K kicks to the right and G jumps to the left, the probability of a goal is 0.9. If K kicks to the left, the probability of a goal is 0.8 if G jumps to the right and 0.5 if G jumps to the left.
Fill the following matrix with the given probabilities. Assume the kicker is the row player and the goalie is the column player.
- What is correct about Nash equilibrium in mixed strategies:
|A.||In a two-player game, mixed strategies are a Nash equilibrium if each player’s mixed strategy is a best response to the other player s mixed strategy, and none will unilaterally deviate.|
|B.||It only exists when all players randomize their pure strategies.|
|C.||Graphically, NE is given by the intersection of the player s best response payoffs|
|D.||In equilibrium, the mixed strategy of a player must put positive probability on a given pure strategy only if the pure strategy is itself a best response to the mixed strategy of the other player.|