In a Bayesian game, the incompleteness of information means that at least one player is unsure of the type ( and so the payoff function ) of another player.
12.
Subsequent work by Heuer discusses a class of games in which the unit square is divided into three regions, the payoff function being constant in each of the regions.
13.
In words, payoff functions in aggregative games depend on players "'own strategies " and the " aggregate " \ sum s _ j.
14.
More recently, viscosity solutions to the infinity Laplace equation have been identified with the payoff functions from "'randomized tug-of-war "'games.
15.
More formally, as before if denotes the set of all options, and we have the payoff function " " " which gives the payoff enjoyed by the agent for each option.
16.
The focal point approach argues that the law cannot change the payoff functions of individuals and the game that people play in life since a law is nothing but some ink on paper ( words written down somewhere ).
17.
The first partial derivative of each payoff function with respect to the follower's ( firm 2 ) strategy variable ( q2 ) and finding its best response function, q2 ( q1 ) = ( 5000-q1-c2 ) / 2.
18.
Here, \ sigma \ in \ Sigma, where \ Sigma = \ Sigma _ i \ times \ Sigma _ {-i }, is a mixed-strategy profile in the set of all mixed strategies and u _ i is the payoff function for player i.
19.
If a player has payoff function U ( x, y ) and he has type t, the payoff he receives is U ( x ^ *, t ), where x ^ * is the strategy profile played in the game ( i . e . the vector of strategies played ).
20.
In static games of cardinal or ordinal utility often cardinal in the normal-form representation ) of a player, i . e . the payoff function of a player takes as its input a strategy profile ( that is a specification of strategies for every player ) and yields a representation of payoff as its output.
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