game theory exam 1

strategy formal definition

strategy definition

a complete plan of action a player can take in a game

strategy profile formal definition

n-tuple of strategies denoted as s = (s1, s2, …, sn) for each player

strategy profile definition

A combination of strategies chosen by all players in a game, where each player selects a strategy based on their available options

Strict dominance formal definition

strict dominance definition

a strategy is strictly dominant for player i if for every possible combination of strategies chosen by the other players, the payoff from choosing that strategy is strictly greater than the payoff from choosing any other strategies

weak dominance definition

Similar to strict dominance, except that in some (but not all) cases, a weakly dominant strategy may yield a payoff equal to that of other strategies, rather than always being strictly better. In other words, weak dominance means that one strategy is never worse and sometimes better than the other strategy, but it's not guaranteed to always outperform it

best reply formal definition

best reply definition

A strategy is a player’s best response to his opponents’ strategies, if given the strategies of the other players, it gives them the highest payoff. Strategy si is the best response to s-i if there is no other strategy that gives player i a better payoff

Nash equilibrium formal definition

Nash equillbrium definition

A Nash Equilibrium is a state where no player has the incentive to unilaterally deviate from their current strategy. In other words, no player can improve their outcome by changing their own strategy, as long as the other players keep their strategies the same

mixed strategy formal definition

mixed strategy definition

A mixed strategy is a probability distribution assigned to each available pure strategy

mixed strategy profile formal definition

mixed strategy profile definition

An n-tuples of mixed strategies, where each player chooses a particular mixed strategy. It consists of the individual mixed strategies of all players in the gam