Zero-Sum Game

A Zero-Sum Game is a competitive game in which a game participant's utility change is exactly balanced by the other game participants' utility change.

• Context:
  • It can typically involve Resource Limitation where zero-sum game total utility remains constant.
  • It can typically create Pure Competition through zero-sum game opposing interests.
  • It can typically require Strategic Decision Making to maximize zero-sum game participant gain.
  • It can typically demonstrate Minimax Principle in zero-sum game optimal strategy.
  • It can typically feature Clear Outcome Distribution where zero-sum game winner gain equals zero-sum game loser loss.
  • It can typically eliminate Cooperation Incentive due to zero-sum game opposing payoff structure.
  • ...
  • It can often incorporate Strategic Deception to gain zero-sum game competitive advantage.
  • It can often require Opponent Move Anticipation for zero-sum game strategy development.
  • It can often serve as Economic Model for zero-sum game resource allocation scenario.
  • It can often showcase Risk-Reward Calculation in zero-sum game decision point.
  • It can often feature Information Asymmetry as a zero-sum game strategic element.
  • It can often create High-Stakes Environment due to zero-sum game necessary loss.
  • ...
  • It can range from being a Two-Player Zero-Sum Game to being a Multiplayer Zero-Sum Game, depending on its zero-sum game participant count.
  • It can range from being a Complete Information Zero-Sum Game to being an Imperfect Information Zero-Sum Game, depending on its zero-sum game information visibility.
  • It can range from being a Deterministic Zero-Sum Game to being a Stochastic Zero-Sum Game, depending on its zero-sum game chance element.
  • It can range from being a Discrete Zero-Sum Game to being a Continuous Zero-Sum Game, depending on its zero-sum game choice granularity.
  • It can range from being a Sequential Zero-Sum Game to being a Simultaneous Zero-Sum Game, depending on its zero-sum game turn structure.
  • It can range from being a Symmetric Zero-Sum Game to being an Asymmetric Zero-Sum Game, depending on its zero-sum game player position equality.
  • ...
  • It can (typically) be a Winner-Take-All Game with zero-sum game complete resource transfer.
  • It can provide Strategic Insight into zero-sum game competitive situation.
  • It can model Conflict Resolution through zero-sum game mathematical formulation.
  • It can serve as Game Theory Cornerstone for studying zero-sum game strategic interaction.
  • It can enable Optimal Strategy Discovery through zero-sum game solution algorithms.
  • ...
• Examples:
  • Traditional Zero-Sum Games, such as:
    • Board Zero-Sum Games, such as:
      • Chess Game demonstrating zero-sum game perfect information strategy.
      • Checkers Game featuring zero-sum game piece capture mechanics.
      • Go Game showcasing zero-sum game territorial control.
    • Card Zero-Sum Games, such as:
      • Poker Game utilizing zero-sum game probabilistic reasoning.
      • Blackjack Game featuring zero-sum game house edge.
      • Bridge Tournament with zero-sum game fixed point scoring.
    • Sport Zero-Sum Games, such as:
      • Tennis Match demonstrating zero-sum game direct opposition.
      • Boxing Contest with zero-sum game physical dominance.
      • Chess Tournament using zero-sum game ranking system.
  • Economic Zero-Sum Games, such as:
    • Financial Zero-Sum Games, such as:
      • Futures Market where zero-sum game contract value transfers between participants.
      • Stock Market transactions where, as noted in the original concept page:
        • a stock transaction cannot both be the right time to sell and the right time to buy.
        • for every unit of currency paid in, a unit of currency comes out.
        • if everyone decided to sell at the same moment (a run on the market) then the price would be zero.
      • Foreign Exchange Market demonstrating zero-sum game currency value transfer.
    • Resource Allocation Zero-Sum Games, such as:
      • Fixed Asset Division requiring zero-sum game fair distribution.
      • Cake Cutting Problem illustrating zero-sum game resource allocation.
      • Auction with zero-sum game single winner.
  • Military Zero-Sum Games, such as:
    • Battlefield Strategy exemplifying zero-sum game territorial control.
    • Arms Race demonstrating zero-sum game security dilemma.
    • Guerrilla Warfare showcasing zero-sum game asymmetric conflict.
  • Mathematical Zero-Sum Games, such as:
    • Matching Pennies illustrating zero-sum game mixed strategy.
    • Colonel Blotto Game featuring zero-sum game resource allocation.
    • Game of Life showing zero-sum game simulated competition.
  • ...
• Counter-Examples:
  • Non-Zero-Sum Games, such as:
    • Cooperative Games like Stag Hunt, where coordination creates greater joint value than individual action.
    • Positive-Sum Games like Trade Agreements, where both parties can achieve mutual benefit.
    • Economic Growth Scenarios where wealth creation expands beyond zero-sum game fixed resources.
    • Labor Markets where employer-employee relationships can create value surplus beyond initial inputs.
    • Innovation Economy where new value creation continually expands the available resource pool.
    • Network Effect Systems where utility increases with each new participant, unlike zero-sum game fixed utility.
  • Mixed-Motive Games, such as:
    • Prisoner's Dilemma featuring both cooperative and competitive elements.
    • Battle of the Sexes containing coordination incentives alongside preference differences.
    • Public Goods Game demonstrating tension between individual gain and collective benefit.
• See: Game Theory, Cake Cutting, Marginal Utility, Minimax Theorem, Nash Equilibrium, Lump of Labor Fallacy, Competitive Equilibrium, Value Transfer, Strategic Dominance.

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References

2014

• http://www.investopedia.com/terms/z/zero-sumgame.asp
  • QUOTE: A situation in which one person’s gain is equivalent to another’s loss, so the net change in wealth or benefit is zero. A zero-sum game may have as few as two players, or millions of participants. Zero-sum games are found in game theory, but are less common than non-zero sumgames. Poker and gambling are popular examples of zero-sum games since the sum of the amounts won by some players equals the combined losses of the others. So are games like chess and tennis, where there is one winner and one loser. In the financial markets, options and futures are examples of zero-sum games, excluding transaction costs. For every person who gains on a contract, there is a counter-party who loses. However, the stock market is not a zero-sum game.

2013

• (Wikipedia, 2013) ⇒ http://en.wikipedia.org/wiki/zero-sum_game Retrieved:2013-12-26.
  • In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which a participant's gain (or loss) of utility is exactly balanced by the losses (or gains) of the utility of the other participant(s). If the total gains of the participants are added up, and the total losses are subtracted, they will sum to zero. Thus cutting a cake, where taking a larger piece reduces the amount of cake available for others, is a zero-sum game if all participants value each unit of cake equally (see marginal utility). In contrast, non–zero sum describes a situation in which the interacting parties' aggregate gains and losses are either less than or more than zero. A zero-sum game is also called a strictly competitive game while non–zero-sum games can be either competitive or non-competitive. Zero-sum games are most often solved with the minimax theorem which is closely related to linear programming duality, or with Nash equilibrium.

1989

• (Friedman et al., 1998) ⇒ Stewart D. Friedman, Perry Christensen, and Jessica DeGroot. (1998). “Work and Life: The End of the Zero-sum Game." Harvard business review 76

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