Strategies
The strategy of a player depends on the position a player has in the game, the first player of a team tries to get two of the same cards (kemps) and the second player tries to avoid getting two same cards, because the team is likely to lose the game when this happens. In order achieve this the players need to reason about their own cards to try to achieve their own goal, but also if they can not immediately reach their goal, they need to avoid that the opponent reaches its goal. This means the players need to think several steps ahead.
Example
When a player is the first player in a team he should always try to get kemps himself first. If this is not possible, he can help his partner by minimizing the probabilities for his partner to get kemps. The player would do this based on his own knowledge of his partners' cards, in other words: the player checks in how many of the accessible Kripke worlds, the next player would possibly get two same cards after a specific action is performed. This will be calculated for all actions and the action with the lowest probability of the partner to get kemps will be selected. A similar process happens when a player is the second player in a team, apart from the fact that this player will avoid to get kemps instead. In the table below priorities for the different players are shown, sorted on importance from high to low.
| Player | Maximize | Minimize |
|---|---|---|
| First Player |
Get Kemps | |
| Next player kemps |
||
| Next next player kemps | ||
| Next next next player kemps |
||
| Second Player |
Get kemps | |
| Next player kemps |
||
| Next next Player kemps | ||
| Next next next player kemps |
Winning a game
The game ends when one of the players calls 'kemps' or 'anti-kemps'. If a player calls kemps and his partner has two same cards, this team wins and if a player calls anti-kemps and one of the opponents has two same cards, then this is the winning team. However, at a false call the other team automatically wins the game.
Signalling
To make sure the partner will call kemps when a player has two same cards, the agents can give eachother signals. The agents of a team agree on the signal before the start of the game, in our implementation the left team uses the word 'tomato' and the right team uses the word 'potato' as a signal. However the teams do not know each other's signal. Therefore it is also possible for agents to give a fake signal to make the opponent agents believe that you have two same cards and make them call 'anti-kemps'. In our implementation these fake signals can be any other word, for example 'strawberry'. The agents can not see the difference between real and fake signals of the opponents, so to be able to tell if a signal is real or fake, the agents reason about what the other agent knows about their cards. This higher-order reasoning is essential to win a game.
The agents will give signals in the following cases:
Calling kemps or anti-kemps
To win a game a player has to call kemps or anti-kemps at the right moment, however a false call will result in losing the game, therefore the agents need to be careful about calling kemps or anti-kemps. An agent will call kemps or anti-kemps in the following cases: