The dice variable represents the outcome of rolling a two-sided dice. We assume that both Arne and Bente are playing with non-skew dice, so for both variables there is a 50% probability to obtain "1" and 50% for "2".
It is pretty easy to convert our guess of Arne's strategy to conditional probabilities. As an example we show the table of AB1:
This task is the most difficult of the three and you are advised to consult net file for the excact tables. The utility functions can be grouped into two:
The first ones are pretty straightforward. In both U5 and U7 it is Arne
who's turn it currently is. For each situation where Arne calls the winner of the game is
determined from the states of the two dice variables. In case Bente wins we assign this
situation a utility value of 1, should Bente lose the utility is set to -1.
Situations where Arne doesn't call are so called "neutral situations" since the
game continues and no winner is found. Hence we assign neutral situations the value 0.
With our
"call->call" trick the situation where both players called corresponds to an already finished game. Bente's outcome has therefore already been found, hence this situation is also assigned the value 0.For U1U4 and U2U6 some extra work has to be done, because it is Bente's
turn. The assigning of values follows the same schema as for U5 and U7: Should Bente
decide to call her outcome is determined.
All the other possible bids are either neutral bids since they don't end the game or
illegal bids. Neutral bids are assigned the value 0 whereas illegal bids are assigned the
value -10 - a real punishment! (the proper value for this situation would be minus
infinity, but -10 will do for our game). We enforce our "call->call"
trick by making all other bids than call illegal actions once Arne called.
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HUGIN Expert A/S | , 1998 |