## Zero-Sum Game

## Definition

In game theory and economic theory, a zero-sum game is a mathematical representation of a situation in which each participant's gain or loss of utility is exactly balanced by the losses or gains of the utility of the other participants. 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.

### Zero-Sum Game

### What is a 'Zero-Sum Game'

Zero-sum is a situation in game theory 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.

### Explaining 'Zero-Sum Game'

In game theory, the game of matching pennies is often cited as an example of a zero-sum game. The game involves two players, A and B, simultaneously placing a penny on the table. The payoff depends on whether the pennies match or not. If both pennies are heads or tails, Player A wins and keeps Player B’s penny; if they do not match, Player B wins and keeps Player A’s penny.

### ‘Zero-Sum Game’ Theory & Background

Game theory is a complex theoretical study in economics. The 1944 groundbreaking work “Theory of Games and Economic Behavior,” written by Hungarian-born American mathematician John von Neumann and co-written by Oskar Morgenstern, is the foundational text. Game theory is the study of strategic decision making between two or more intelligent and rational parties. The theory, when applied to economics, uses mathematical formulas and equations to predict outcomes in a transaction, taking into account many different factors, including gains, losses, optimality and individual behaviors.

### ‘Zero-Sum Game’ & Economics

When applied specifically to economics there are multiple factors to consider when understanding a zero-sum game. Zero-sum game assumes a version of perfect competition and perfect information; that is, both opponents in the model have all the relevant information to make an informed decision. To take a step back, most transactions or trades are inherently non zero-sum games because when two parties agree to trade they do so with the understanding that the goods or services they are receiving are more valuable than the goods or services they are trading for it, after transaction costs. This is called positive-sum, and most transactions fall under this category.

### Further Reading

**Swaps: A zero sum game?**

www.jstor.org [PDF]

… Stuart M. Turnbull Stuart M. Turnbull is Associate Professor of Economics and Finance, University of Toronto … TURNBULL/SWAPS: A ZERO SUM GAME? 21 … 3. J. Bicksler and AH Chen, "An Economic Analysis of Interest Rate Swaps," Journal of Finance (July 1986), pp. 645-655 …

**Secured Lending as a Zero-Sum Game**

heinonline.org [PDF]

… Stuart M. Turnbull Stuart M. Turnbull is Associate Professor of Economics and Finance, University of Toronto … TURNBULL/SWAPS: A ZERO SUM GAME? 21 … 3. J. Bicksler and AH Chen, "An Economic Analysis of Interest Rate Swaps," Journal of Finance (July 1986), pp. 645-655 …

**College sports: The mystery of the zero-sum game**

www.tandfonline.com [PDF]

… Stuart M. Turnbull Stuart M. Turnbull is Associate Professor of Economics and Finance, University of Toronto … TURNBULL/SWAPS: A ZERO SUM GAME? 21 … 3. J. Bicksler and AH Chen, "An Economic Analysis of Interest Rate Swaps," Journal of Finance (July 1986), pp. 645-655 …

**The euro versus the dollar: not a zero sum game**

www.sciencedirect.com [PDF]

… Stuart M. Turnbull Stuart M. Turnbull is Associate Professor of Economics and Finance, University of Toronto … TURNBULL/SWAPS: A ZERO SUM GAME? 21 … 3. J. Bicksler and AH Chen, "An Economic Analysis of Interest Rate Swaps," Journal of Finance (July 1986), pp. 645-655 …

**Is women empowerment a zero sum game? Unintended consequences of microfinance for women's empowerment in Ghana**

www.emerald.com [PDF]

… Stuart M. Turnbull Stuart M. Turnbull is Associate Professor of Economics and Finance, University of Toronto … TURNBULL/SWAPS: A ZERO SUM GAME? 21 … 3. J. Bicksler and AH Chen, "An Economic Analysis of Interest Rate Swaps," Journal of Finance (July 1986), pp. 645-655 …

**Service productivity vs service quality: a zero-sum game?**

www.emerald.com [PDF]

… Stuart M. Turnbull Stuart M. Turnbull is Associate Professor of Economics and Finance, University of Toronto … TURNBULL/SWAPS: A ZERO SUM GAME? 21 … 3. J. Bicksler and AH Chen, "An Economic Analysis of Interest Rate Swaps," Journal of Finance (July 1986), pp. 645-655 …

**South Africa in GEAR:'A better life for all'or a zero-sum game of globalization?**

link.springer.com [PDF]

… Stuart M. Turnbull Stuart M. Turnbull is Associate Professor of Economics and Finance, University of Toronto … TURNBULL/SWAPS: A ZERO SUM GAME? 21 … 3. J. Bicksler and AH Chen, "An Economic Analysis of Interest Rate Swaps," Journal of Finance (July 1986), pp. 645-655 …

**Going beyond a zero-sum game: reforming fiscal relations**

heinonline.org [PDF]

… Stuart M. Turnbull Stuart M. Turnbull is Associate Professor of Economics and Finance, University of Toronto … TURNBULL/SWAPS: A ZERO SUM GAME? 21 … 3. J. Bicksler and AH Chen, "An Economic Analysis of Interest Rate Swaps," Journal of Finance (July 1986), pp. 645-655 …