The tempted sentinel game

Micro controllers
Vector graphics
Joakim Linde (2003), Iterated games as models of alarm calling. Licentiate thesis. Chalmers University of Technology.

The tempted sentinel game is a model of deception in alarm calls in the form of an indefinitely iterated two person signaling game. Single rounds of the game are asymmetric with a sender-player and a receiver-player. However, the iteration of the game will make it symmetric on the whole. Both players are feeding, but the sender has a better view of the surroundings than the receiver. Consequently the sender will spot approaching predators before the receiver does. A single round of the game proceeds as follows:
  1. Determine player roles. There are two different roles for players. One player will act as sender, while the other acts as receiver. The allocation of player roles is done randomly and independently at the beginning of each round. Both players have the same probability for playing the sender role.
  2. Determine the state of the environment. There are two possible environmental states, E_1 (no predator is nearby) and E_2 (a predator is nearby). The state of the environment is determined randomly and independently each turn, with probability p for state E_2 and probability (1-p) for state E_1.
  3. Sender signals. In this step the sender is allowed to observe the state of the environment and can choose to send signal S_1 (no signal) or signal S_2 (alarm call). The alarm call S_2 has a cost C > 0, while signal S_1 is costless.
  4. Receiver responds. The receiver is allowed to observe the signal, but is not allowed to observe the state of the environment. After the signal type has been determined the receiver must choose to perform action A_1 (continue feeding) or perform action A_2 (anti-predator response).
  5. Determine payoff. The payoffs for both sender and receiver depend on the state of the environment, the signal type and the action performed by the receiver. The payoff is expressed using the game parameters T, C and U. The value of feeding for one round is set to 1 and sets the scale of the payoff. Should the receiver, for some reason, stop feeding it is possible for the sender to take advantage of that. The sender will then receive a payoff of 1+T instead. Performing anti-predator response gives both players a payoff of 0. Senders are assumed to always perform anti-predator response when a predator has been spotted (state E_2). Receivers, on the other hand, may fail to perform an appropriate anti-predator response, when the environment is in state E_2, and in that case receive a payoff of -U.
  6. Go to step 1. The game is iterated indefinitely and the expected payoff per turn is used to determine the fitness of a player.