Bayesian game: Difference between revisions

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m replace misleading plural by singular: utility takes as argument "type and action profile", not "type and action profiles".
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# '''Action sets, ''a<sub>i</sub>'':''' The set of actions available to Player ''i''. An action profile ''a = (a<sub>1</sub>, . . . , a<sub>N</sub>)'' is a list of actions, one for each player
# '''Type sets, ''t<sub>i</sub>'':''' The set of types of players ''i''. "Types" capture the private information a player can have. A type profile ''t = (t<sub>1</sub>, . . . , t<sub>N</sub>)'' is a list of types, one for each player
# '''Payoff functions, ''u'':''' Assign a payoff to a player given their type and the action profilesprofile. A payoff function, ''u= (u<sub>1</sub>, . . . , u<sub>N</sub>)'' denotes the utilities of player ''i''
# '''Prior, ''p'':''' A probability distribution over all possible type profiles, where ''p(t) = p(t<sub>1</sub>, . . . ,t<sub>N</sub>)'' is the probability that Player 1 has type ''t<sub>1</sub>'' and Player ''N'' has type ''t<sub>N</sub>''.