Game Theory: Types, Nash Equilibrium, and Classic Models Explained

Based on the book "Game Theory: Everyone Can Become a Decision‑Making Expert" by Jiang Wenhua, this article explains the basic concepts, classifications, and applications of game theory across economics, politics, sociology, and management.

1. Overview

1) Game Types and Structured Thinking

Games can be classified by their structure: static vs. dynamic, and complete vs. incomplete information.

Static and Dynamic Games

Static games : Players choose simultaneously or without knowing others' actions.

Dynamic games : Players act sequentially and later players observe earlier actions.

Examples: Rock‑paper‑scissors and bidding are static games; board games and auctions are dynamic games.

In a school rating scenario where teachers and students rate each other, the process is a static game because the first mover’s rating is hidden from the other party.

Difference : In static games, decisions are based on imagined opponent strategies; in dynamic games, decisions are based on observed actions.

Complete and Incomplete Information Games

Complete information : All players know each other's types, strategy spaces, and payoff functions.

Incomplete information : Some information is hidden from one or more players.

Real‑world examples: Education, healthcare, and finance are typically incomplete‑information games, while truly complete‑information games are rare.

Structured Thinking

When an object can be classified along multiple dimensions, combining those dimensions creates a structured, two‑dimensional representation, useful for analyzing game types.

2) Expanded Cognition

Nash Equilibrium

Equilibrium is the optimal strategy combination for all participants. Nash equilibrium means each player's strategy is the best response to the others' strategies, and no player has an incentive to deviate. In short : Neither side wants to move away from the equilibrium state.

Strategy Exploration

Strategies have three main attributes:

Completeness : All possible situations are considered.

Diversity : Multiple alternative plans are available.

Unobservability : Strategies are plans, not actions; they may be misinterpreted.

Emergency Plan Four Elements

Clear, complete information classification.

Responsibility assigned to specific individuals.

Pre‑prepared, feasible action plans.

Timeliness: explicit time requirements for each action.

Rational Assumptions

Rationality is broad; three standards are:

Complete preference and contextual rationality : Preferences depend on the specific context (e.g., pricing of digital vs. print versions).

Example pricing scenarios (Plan A and Plan B) illustrate how context influences consumer choices.

All judgments are based on a reference frame; different frames lead to different decisions.

Transitivity of preferences : If A > B and B > C, then A > C.

Violating transitivity leads to random, unpredictable choices.

Moderation of preferences : If A and B are equally liked, a middle option C is preferred.

Common Knowledge

Common knowledge means everyone knows a fact, knows that everyone else knows it, and so on. It differs from shared knowledge, which is merely known by all.

In the “two‑generals problem” and TCP three‑way handshake, common knowledge is essential for coordination.

3. Classic Models

1) Coward Game

Both players gamble on who will retreat first; the first mover advantage is decisive.

2) Spouse Game

Deciding where to celebrate the New Year can have two pure‑strategy Nash equilibria (both go to the husband's family or both to the wife's family) or mixed solutions.

3) Prisoner’s Dilemma

Two suspects are interrogated separately; mutual silence yields a light sentence, but each has an incentive to betray, leading to a worse outcome for both.

Dominant strategy : A strategy that yields better outcomes regardless of the opponent’s choice.

4) 10,000‑Yuan Trap

A bidding game where the highest bidder wins the prize, but the second‑highest also pays their bid, leading participants to over‑bid and potentially incur huge losses.

Avoid the trap by setting a clear loss limit and not chasing unrealistic gains.

5) Pig Game (Smart Pig)

Two pigs share a food source; the larger pig can press a button to obtain food, while the smaller pig may wait. The Nash equilibrium is the large pig pressing the button and the small pig waiting.

Key insights: individual rationality vs. collective rationality depends on institutional design; unequal income distribution can exacerbate conflicts.

Pure vs. Mixed Strategies

Pure strategy : A single specific action chosen in every situation.

Mixed strategy : Randomized selection of actions according to a probability distribution.

Example: “If you don’t harm me, I won’t harm you” (pure); “I will not harm you with 80% probability” (mixed).

6) Deer Hunt Game

Two hunters can either hunt rabbits individually (2 rabbits total) or cooperate to hunt a deer (value equivalent to 8 rabbits). Cooperation yields higher payoff if communication costs are low.

Life is full of games; understanding game theory provides a forward‑looking perspective for rational decision‑making.

For further reading, see the linked articles on microservice architecture and related topics.