This page shows an example run of a single game and aims to give insight in the changes in the accessible Kripke worlds of an agent during a game. For this we focus on 'player 1', but the processes are the same for all players.
Initialization
At the initialization of the game player 1 knows which 10 cards are in the game, moreover he knows his own 2 cards and the 2 cards that lay on the table. However, he does not yet have any knowledge about how the other 6 cards are divided among the 3 other players. Therefore the knowledge about the cards of these three players is exactly the same. This knowledge form the accessible Kripke worlds, in which every possible combination of cards is a single accessible Kripke world. The table below shows the knowledge of player 1 after the initialization of this sample game.
| Initial knowledge of Player 1 |
|
|---|---|
| Player 1 |
[[4, 5]] |
| Player 2 |
[[2, 2], [4, 3], [4, 5], [5, 2], [1, 1], [1, 3], [1, 2], [1, 5], [3, 5], [3, 2], [3, 3], [4, 2], [4, 1]] |
| Player 3 |
[[2, 2], [4, 3], [4, 5], [5, 2], [1, 1], [1, 3], [1, 2], [1, 5], [3, 5], [3, 2], [3, 3], [4, 2], [4, 1]] |
| Player 4 |
[[2, 2], [4, 3], [4, 5], [5, 2], [1, 1], [1, 3], [1, 2], [1, 5], [3, 5], [3, 2], [3, 3], [4, 2], [4, 1]] |
| Table | [[2, 2], [4, 3], [4, 5], [5, 2], [1, 1], [1, 3], [1, 2], [1, 5], [3, 5], [3, 2], [3, 3], [4, 2], [4, 1]] |
Turn of player 2
At the start of a turn a player chooses a card to swap, how a player chooses a card is described in more detail on the strategies page. After player 2 chooses cards to swap, the cards are swapt and the knowledge about the game is updated. In our sample game, player 2 did swap a card with the table, however because player 1 can not see the actions of player 2, there is no change in the knowledge of player 1.
Turn of player 3
A turn of player 3 is for a large part the same as a turn of player 2, but now player 1 can see which cards player 3 swaps. Therefore an action of player 3 reduces the Kripke worlds that are accessible for player 1. The table below shows this updated knowledge of player 1 after the turn of player 3.
| Knowledge of Player 1 after the turn of Player 3 |
|
|---|---|
| Player 1 |
[[4, 5]] |
| Player 2 |
[[3, 5], [3, 2], [3, 3], [4, 3], [4, 5], [5, 2], [4, 2], [4, 1], [1, 1], [1, 3], [1, 2], [1, 5]] |
| Player 3 |
[[5, 2], [4, 2], [3, 2], [1, 2]] |
| Player 4 |
[[3, 5], [3, 2], [3, 3], [4, 3], [4, 5], [5, 2], [4, 2], [4, 1], [1, 1], [1, 3], [1, 2], [1, 5]] |
| Table | [[3, 5], [3, 2], [4, 3], [4, 5], [5, 5], [5, 1], [5, 2], [4, 2], [4, 1], [3, 1], [1, 1], [1, 2] |
Turn of player 4
Player 4 is the teammate of Player 1, but Player 1 can not see the swap action of Player 4 and therefore the knowledge of Player 1 will not update after this turn. However, player 4 says anti-kemps and the game ends. On the screen is showed that player 2 and 3 win the game, because the kemps call was false.