What Is a Game

WHAT IS A GAME? game theory — the math of strategic interdependence: choosing when the best move depends on what everyone ELSE chooses 1 · WHAT MAKES IT A GAME PLAYER 1 PLAYER 2 each choice affects the other 4 ingredients: • PLAYERS — the decision-makers • STRATEGIES — the moves each one can make • PAYOFFS — what each gets for every combination • RATIONALITY — each maximises its OWN payoff, and knows the others do too (common knowledge). a DECISION becomes a GAME when your best move depends on THEIR move — and theirs on yours. 2 · THE PAYOFF MATRIX (normal form) THEM Left Right YOU Up Down (3, 2) (0, 0) (0, 0) (2, 3) read a cell (a, b): a = YOUR payoff, b = THEIRS (yours first). you pick a ROW, they pick a COLUMN — at the same time. the chosen cell is the outcome. here top-left = you 3 / them 2. 3 · ZERO-SUM vs NON-ZERO-SUM — is the pie fixed? ZERO-SUM a FIXED pie. my slice bigger = yours smaller. payoffs sum to a constant. poker, chess, splitting a set budget. → pure competition. NON-ZERO-SUM the pie can GROW (positive-sum: trade, teamwork) or SHRINK (negative-sum: war, arms race). → most of real life. the classic error: treating a NON-zero-sum situation (a team, a vendor deal) as zero-sum → you fight over slices instead of GROWING the pie. spot the pie first. 4 · SIMULTANEOUS vs SEQUENTIAL — matrix or tree? SIMULTANEOUS — both move at once, blind to the other. the NORMAL FORM (a matrix). rock-paper-scissors, sealed bids. SEQUENTIAL — players move in TURN; later sees earlier. the EXTENSIVE FORM (a game tree). chess, negotiation. → look ahead & reason BACKWARD (backward induction, board 02). same game, two pictures. which one fits depends on whether the players can see each other's move before choosing. a strategy is a COMPLETE plan: what you'd do at EVERY point you might have to act — not just your next move. 5 · WHAT DO THE PLAYERS KNOW? PERFECT info — you see every move so far (chess). IMPERFECT — hidden moves (poker, simultaneous choices). COMPLETE info — everyone's payoffs are known. INCOMPLETE — you don't know their payoffs / 'type' (auctions, bluffing, hiring). THE RATIONALITY CAVEAT game theory assumes players are perfectly rational, self-interested payoff-maximisers. real humans aren't — see the Psychology track: biases "Cognitive Biases" & prospect theory "Decision-Making Under Uncertainty". so treat it as the RATIONAL BASELINE — the prediction if everyone plays optimally. 'behavioural game theory' then adds the human wrinkles (spite, fairness, trust, limited foresight) on top. the four axes — payoffs, timing (simultaneous/sequential), information, rationality — fully specify any game. everything else is solving it. GAMES ARE EVERYWHERE IN SYSTEMS (shop / Agent) • RATE LIMITING = a game: your service vs abusers, each adapting to the other's policy. AD / SPECTRUM AUCTIONS = literal games with designed payoff rules (board 07). • RESOURCE CONTENTION: two services grabbing cluster capacity is a game — uncoordinated, both can lose (a negative-sum thrash). Backoff/quotas are the rules that fix the payoffs. • DISTRIBUTED CONSENSUS: nodes as players who must agree despite failures/liars → the payoff structure is engineered so honesty is the best strategy (mechanism design, board 07). • NEGOTIATION (vendors, teams, salary): almost always NON-zero-sum — name the pie before you carve it, or you'll bleed value fighting over slices. JARGON, DECODED strategy — a complete plan of action, for every situation payoff — the value a player gets from an outcome normal form — the payoff matrix (simultaneous games) extensive form — the game tree (sequential games) zero-sum — payoffs sum to a constant; pure competition positive / negative-sum — the pie grows / shrinks common knowledge — everyone knows it, knows they know... perfect / imperfect info — moves visible / hidden rationality — each maximises its own payoff (the baseline)