Dominance Interactions & Game Theory

Game Theory

• Evaluation is via Game Theory
• Developed by Maynard-Smith, based on economic theory
• The solution to the 'game' is the evolutionary stable strategy 
  • A strategy which, when adopted by most members of the population, cannot be beaten by any other strategy in the game.

Analysis of Fighting Strategies

• What is the most successful fighitng strategy?
• Why are some fights ritualised displays and others physical contact?
• Evolution should favour displays
• Strategies can't be evaluated using a simple optimality model of costs and benefits as the optimal way for one individual to behave depends on what other competitors are doing.

Hawks and Doves

• Imagine a contest over a resource (e.g. habitat) with 2 extreme strategies:
• Hawk
  • Always fight to injure and kill your opponent - possible risk of injury to self
• Dove
  • Display but never engage in a serious fight - i.e. run away when opponenet escaltes fight

Fight outcomes

• Hawk vs Hawk
  • Each contestant has a 50% chance of injuring opponent and winning resource, and 50% chance of being injured.
• Hawk vs Dove
  • Hawk always wins resource
• Dove vs Hawk
  • Dove retreats immediately before injury
• Dove vs Dove
  • Resource is shared

Payoff Matrix

How would evolution proceed?

• If all individuals were Doves....
  • Everyone has an average payoff of 25
  • But a mutant Hawk has a payoff of 50 so would do very well
  • Dove is not an Evolutionary Stable Strategy as it can be invaded by Hawks
• …