Introduction to Strategic Game Theory and Payoff Modeling

Game theory is the modeling of strategic interactions, defined as social environments where all participants are aware that their actions affect the payoffs of others and themselves.
A strategy is an action or a set of actions (action plan) chosen by a player within this interaction.
A game acts as the economic model of a specific strategic interaction, such as the airline pricing competition between Qantas and Virgin.

Players: The set of entities involved in the interaction, identified in the example as Qantas, Inversion, and Virgin.
Feasible Strategies: The available actions for each player; in the provided example, each airline can set a price as High or Low.
Order of Play: The sequence in which players choose actions.
Information: What each player knows regarding the game structure and other players' decisions at the time of their own choice.
Payoffs: The specific outcomes for each player resulting from every possible combination of actions.

Simultaneous Game: Players make decisions without knowledge of other players' choices. It is characterized by the information state rather than specific visual timing.
Sequential Game: Timing dictates that players moving later have information about the actions chosen by those who moved before them.
Full Information: The assumption that all players know the structure of the game, every player's options, and all potential payoffs.

Normal Form (Game Box): A tool for structuring simultaneous games consisting of a Row player (e.g., Qantas) and a Column player (e.g., Virgin).
Payoff Notation: Payoffs are listed in pairs where the first number represents the Row player and the second represents the Column player.
Airline Pricing Example Data: * Passengers: $100$ * High price: $100$ * Low price: $75$
Distribution Rules: * Same Price: Players split passengers ( $50$ each). * Divergent Prices: The player with the Low price takes all $100$ passengers.
Calculated Payoffs: * Both High: ( $5000$ , $5000$ ) based on $50 \times 100$ * Both Low: ( $3750$ , $3750$ ) based on $50 \times 75$ * One Low/One High: ( $7500$ , $0$ ) or ( $0$ , $7500$ ) based on the Low-setter capturing $100 \times 75$