Game Theory Presented by Abigail Atiwag Game theory is a branch of mathematics and economics that studies strategic interactions among rational decision makers It provides a framework for analyzing how individuals firms or governments make decisions in competitive situations where the outcome of one s decision depends on the decisions of others Key concepts and topics in game theory include Players In game theory players are the decision makers involved in the strategic interaction They could be individuals firms countries or any entity making choices that affect outcomes Strategies A strategy is a plan of action chosen by a player to achieve their objectives in a game It specifies what actions the player will take in different possible situations or scenarios Payoffs Payoffs represent the outcomes or consequences of the players actions in a game They can be in the form of rewards profits utility or any measurable outcome that reflects the players preferences Normal Form Games Normal form games also known as strategic form games are represented by a matrix that shows the players strategies and payoffs Each cell in the matrix corresponds to a combination of strategies chosen by the players and the resulting payoffs Nash Equilibrium A Nash equilibrium is a situation in which each player s strategy is optimal given the strategies chosen by the other players In other words no player has an incentive to unilaterally deviate from their strategy if others stick to their strategies Dominant Strategy A dominant strategy is a strategy that yields the highest payoff for a player regardless of the strategies chosen by other players Players with dominant strategies will always choose those strategies regardless of the actions of others Mixed Strategies In some games players may randomize their strategies to achieve better outcomes A mixed strategy is a probability distribution over the player s possible pure strategies indicating the likelihood of choosing each strategy Zero Sum Games Zero sum games are games where the total payoff to all players remains constant meaning one player s gain is exactly balanced by another player s loss Examples include many competitive games like chess or poker Cooperative Games Cooperative games involve players who can form coalitions or alliances to achieve joint objectives and share the resulting payoffs Cooperative game theory studies how players can cooperate and negotiate to achieve mutually beneficial outcomes Sequential Games In sequential games players make decisions sequentially with each player observing the actions of previous players before making their own decisions Examples include games with a first mover advantage or games with a specific order of play Repeated Games Repeated games involve multiple rounds of play where players can learn from past interactions build reputations establish cooperation or competition patterns and strategically adjust their strategies over time Game Theory Applications Game theory has applications in various fields such as economics pricing strategies auctions industrial organization political science voting behavior bargaining international relations biology evolutionary game theory animal behavior computer science algorithm design network protocols and psychology strategic decision making social interactions Overall game theory provides a powerful analytical tool for understanding strategic interactions predicting outcomes designing optimal strategies and studying complex decision making processes in competitive or cooperative environments THANK YOU