#### Title

Evolutionary Game Theory and Evolutionarily Stable Strategies

#### Academic Level at Time of Presentation

Sophomore

#### Major

Mathematics

#### Minor

Biology

#### List all Project Mentors & Advisor(s)

Maeve McCarthy

#### Presentation Format

Oral Presentation

#### Abstract/Description

The object of game theory is to choose a strategy that will resolve conflicts, with the highest payoff for all individuals involved. In this presentation, two scenarios of game theory are analyzed: 2 player-2 choice game theory, and 2 player-3 choice game theory, demonstrated by Hawk-Dove game theory and Rock-Paper-Scissors game theory, respectively. The payoffs of every matchup within each scenario are evaluated. Then, both scenarios are analyzed to find an evolutionary stable strategy (ESS), which is a set of strategies, one for each player, such that no player has the incentive to deviate given what the others are doing. Interestingly, we find that because always choosing a pure strategy does not maximize benefit, these evolutionary stable strategies and selection from these strategies are actually a mechanism behind the consistent balance of different characteristics in a population.

Keywords: game theory, equilibrium, competition, population

#### Spring Scholars Week 2018 Event

Projects in Biomathematics (BIO/MAT 460)

Evolutionary Game Theory and Evolutionarily Stable Strategies

The object of game theory is to choose a strategy that will resolve conflicts, with the highest payoff for all individuals involved. In this presentation, two scenarios of game theory are analyzed: 2 player-2 choice game theory, and 2 player-3 choice game theory, demonstrated by Hawk-Dove game theory and Rock-Paper-Scissors game theory, respectively. The payoffs of every matchup within each scenario are evaluated. Then, both scenarios are analyzed to find an evolutionary stable strategy (ESS), which is a set of strategies, one for each player, such that no player has the incentive to deviate given what the others are doing. Interestingly, we find that because always choosing a pure strategy does not maximize benefit, these evolutionary stable strategies and selection from these strategies are actually a mechanism behind the consistent balance of different characteristics in a population.

Keywords: game theory, equilibrium, competition, population