~ a science of strategic interactions ~
Non-Zero-Sum games are just one aspect of the wider field of Game Theory; a fascinating field of mathematics that deals with models of conflict and cooperation among rational decision-makers.
While humans have used game-theoretical ideas throughout history, Game Theory was formalised by John von Neumann and economist Oskar Morgenstern in their seminal work, "Theory of Games and Economic Behavior", in 1944.
KEY CONCEPTS IN GAME THEORY
Here are some pivotal ideas in the study of game theory:
Player: Anyone with skin in the game, like a team member in a football game, a CEO in corporate politics, or even countries in global diplomacy.
Strategy: Your plan of action, whether you're lining up behind a spawn point or planning a long-term business model.
Payoff: What you get out of it, from winning a bet to securing a long-term business contract.
TYPES OF GAMES
Where one's loss is another's gain, from a tug-of-war to legal battles. Zero-Sum Game:
Win-win situations, like mutually beneficial trade agreements or collaborative research projects. Non-Zero-Sum Game:
Simultaneous Game: Players act at the same time, from Rock-Paper-Scissors to blind auctions.
Sequential Game: Where Players take turns, like chess.
No chance moves and perfect information, like chess, connect four, or Combinatorial Games: Square Bears
STRATEGIES AND EQUILIBRIA
No one can benefit from changing their strategy if others don't, like stopping at traffic lights, or driving on the correct side of the road. Nash Equilibrium:
Dominant Strategy: A strategy that guarantees a win or draw: Like defecting in the a single round of the Prisoner's Dilemma. A rare example of tic-tac-toe has a dominant strategy right from the start for both players that always leads to a draw - making it a very limited game. Often dominant strategies will become available at a point of leverage in a game, like two rooks against a king reveals the strategy of driving the king to the end of the board.
Dominated Strategy: The always worse option, like folding in poker no matter your hand, always choosing the defensive play in football or camping in a deathmatch.
Mixed Strategy: Introducing randomness, from mixing up your serves in tennis to changing up your pricing strategy in a bidding war.
Mechanism Design: Creating game rules to get desired outcomes, from designing balanced gameplay in a video game to optimizing voting systems.
When it's not possible to make one player better off without making another player worse off the situation is Pareto Efficient - like when you're swapping cards and no one has any doubles that the other needs. Pareto Efficiency:
Common Knowledge: Information that everyone knows and understands, like the basic rules of chess or commonly accepted business practices.
A very complex algorithm for divvying up payoffs fairly in cooperative scenarios, like joint business ventures or splitting bills among roommates. Shapley Value:
Extensive Form: Using tree-like diagrams to map sequential moves, useful in chess and corporate decision-making.
Normal Form: Using a matrix for simultaneous moves, handy in figuring out everything from the prisoner's dilemma to market competitions.
Each of these concepts provides a unique lens through which to understand the dynamics of various types of games, from simple games like tic-tac-toe to complex economic and social interactions. What concept fascinates you the most? What would you like to explore further?
Leave us your thoughts below.