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Game Theory

Game theory usually attempts to determine what will happen when two or more agents cooperate/compete in trying to maximize their own expected utility.

Decision theory prescribes how one agent should best make decisions to maximize his expected utility, given his beliefs about the environment and how other agents will act.

If you specify the behavior (as a probabilistic policy) of the other players involved in a game, then you can use decision theory to determine how one player should best act.  But it won’t determine the policies for all players simultaneously like game theory sometimes will.  Currently Netica only solves decision theory problems.  It can still be a valuable tool for investigating game theory problems, but only from one player's point of view (rather than a global point of view).

If you want to use Netica to formulate a game, then make a decision node for a single player and a nature node for each of the other players.  Use the table dialog box to enter a policy for each of the other players.  There will be links between these nodes only if some players will know what some other players actions are before making their own decision.

Then add a utility node, with links from each of the other nodes to it.  You can fill the utility node table quite easily from the game theory payoff matrix (it will have one row for each cell of the matrix) by keeping in mind that you are only entering the payoff for the single player you are analyzing.  Supposedly the other payoffs were used to determine the policies for the other players, perhaps using another decision net.

You may find that you want to iterate solutions, since developing each player's decision net depends on the policies of other players, which you don't know until you have solved their decision nets, which require the policy (solution) of the first net.  You may find Netica API useful to write a program for such iterations (or to explore how strategies and policies of a population evolve over time).
 

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