As part of the game theory student seminar our team played the Split-Steal game in class.
Two players with two actions each, Split or Steal. The treasure was comically 2 gingerbread cookies!
Essentially a form of Hawk-Dove game. Hawk: aggressive (escalates conflict) i.e. Steals , Dove: non-aggressive (backs down from escalation) so naturally Splits.
Different strategies / roles
- Hawk: Aggressive, never retreats.
- Dove: Defensive, retreats if opponent is aggressive.
- Bully: Aggressive against defensive opponents. Retreats if opponent is too aggressive.
- Retaliator: Defensive, but retaliates aggressively if opponent is aggressive.
- Prober-retaliator: Defensive, but sometimes makes aggressive probes and only reverts to defensive if the response is aggressive. Retaliates aggressively if opponent is aggressive.
CLICK ON THE LINKS BELOW TO WATCH THE VIDEOS OF THE GAME:
Final Part of the game:
More parts of the seminar
This game can also be seen as a Bayesian game. Information about characteristics or types of the other players (i.e. payoffs) is incomplete in such games. Nature assigns a random variable to each player which could take values of types for each player and associating probabilities (or a probability density function with those types). At least one player is unsure of the type and the payoffs of another player. Players have initial beliefs about the type of each player and can update their beliefs according to Bayes' Rule as play takes place in the game. The belief a player holds about another player's type might change on the basis of the actions they have played.
In a Bayesian game setting there are three meaningful notions of expected utility: ex post, ex interim and ex ante.
- Ex post: Here EU is computed based on all agents’ actual types (rarely feasible as even the game being played maybe unknown at times)
- Ex interim: Considers the setting in which an agent knows his own type but not the types of the other agents (more practical)
- Ex ante: In this case the agent does not know anybody’s type including her own
Analysis of the Game: