Within the broader scope of game theory, the payoff matrix stands as a fundamental yet simple framework for analyzing the outcomes of strategic decisions involving multiple players. But why is this table still widely used in macroeconomics, including governments, central banks, and financial institutions? In today’s increasingly complex and interconnected economic landscape, let us explore why this simple yet foundational tool continues to offer valuable insights into decision-making and policy impact.

What is a payoff matrix in game theory?

Just as its name suggests, a payoff matrix is a structured table used to illustrate the possible strategies and outcomes (the ‘payoff’) when two or more players make decisions simultaneously. Each cell in the matrix represents the resulting payoff for all players based on the combination of choices made. This format helps clarify which outcomes are more advantageous, with the higher number in each cell typically indicating the more favorable result for that player.1

A general example for a two-player scenario is as follows:

 

 

Firm B: Advertise (A)

Firm B: Advertise (A)

Firm B: Not Advertise (B)

Firm B: Not Advertise (B)

 

Firm A: Advertise (A)

Firm A: Advertise (A)

Firm B: Advertise (A)

($30k, $30k)

Firm B: Not Advertise (B)

($50k, $20k)

 

Firm A: Not Advertise (N)

Firm A: Not Advertise (N)

Firm B: Advertise (A)

($20k, $50k)

Firm B: Not Advertise (B)

($40k, $40k)

Table 1: Illustrative example – Strategic advertising payoffs

The illustration above shows all possible outcomes for Firm A and Firm B’s profits depending on their advertising decisions. If both firms choose to advertise at the same time and spend money to compete, they earn similar, moderate profits. If one firm advertises while the other doesn’t, the advertiser gains a competitive edge and earns more. If both choose not to advertise, they avoid costs and split the market evenly. By utilizing this framework, both parties can identify dominant strategies and determine the Nash equilibrium to support more informed, strategic decision-making.2

Why is the payoff matrix important in macroeconomics?

The payoff matrix is a valuable tool in macroeconomics as it offers policymakers and economists a visual method to analyze situations and potential outcomes when multiple agents influence each other.3 It is important to note that complex economic scenarios often involve highly interdependent parties, such as countries engaged in trade negotiations, central banks forming monetary agreements, or large firms competing in an oligopoly.4

Given the large number of parties involved, the ability to accurately analyze these interactions and formulate sound strategic decisions is paramount. A well-constructed matrix supports better forecasting of policy outcomes, reveals incentives for cooperation or rivalry, helps assess the risk-reward trade-offs of strategy combinations, and offers insight into when and how a Nash equilibrium might arise in dynamic, multi-actor environments.5

How payoff matrices work in macroeconomics

While payoff matrices can be applied across a range of macroeconomic scenarios, the following examples illustrate how they enable clearer visualization and more structured analysis of the potential outcomes tied to different policy or strategic decisions.

Interest rate coordination between central banks

The matrix can be a tool to showcase how strategic coordination of interest rates can influence capital flows, exchange rate dynamics, and financial stability across countries.6 This is because in today’s interconnected global economy, major central banks adjust their interest rate not in isolation. While raising rates independently may help control inflation, it also risks slowing global demand and affecting perceptions of the country.6 At the same time, holding rates steady can help support broader economic activity across borders.

Below is a hypothetical illustration showing the possible outcomes when two major central banks (A and B) each decide whether to raise or hold interest rates. The outcomes are measured in basis points (bps) of annual GDP growth. For example, +50 bps represents approximately a 0.5% increase in annual GDP growth. 

 

 

Central Bank B: Raise rates

Central Bank B: Raise rates

Central Bank B: Hold rates

Central Bank B: Hold rates

 

Central Bank A: Raise rates

Central Bank A: Raise rates

Central Bank B: Raise rates

(+25bps, +25bps)

Central Bank B: Hold rates

(0bps, +50bps)

 

Central Bank A: Hold rates

Central Bank A: Hold rates

Central Bank B: Raise rates

(+50bps, 0bps)

Central Bank B: Hold rates

(+50bps, +50bps)

Table 2: Illustrative example - interest rate coordination between central banks

When both countries either raise or hold interest rates simultaneously, they achieve balanced and positive outcomes for their annual GDP growth. However, asymmetric policy choices lead to uneven capital flows. The country that holds rates tends to benefit in the short term, as its relatively lower interest rates attract capital and make borrowing more appealing, such as for individuals taking out mortgages to build homes or for businesses planning to expand domestically.7

Banking regulation across jurisdictions

This game theory matrix also illustrates the outcomes of banking regulation across multiple jurisdictions. When jurisdictions implement comparable regulatory standards, they help foster a more stable and resilient financial system, as shown by post-crisis experience throughout the past century.8 However, if one country adopts looser regulations to attract businesses, this can lead to regulatory arbitrage and the emergence of systemic risk.

Below is a simplified illustration of two hypothetical countries (A and B) deciding whether to implement strict or light-touch banking regulations, with outcomes measured in billions of dollars ($) of capital.

 

 

Country B: Strict regulation

Country B: Strict regulation

Country B: Light regulation

Country B: Light regulation

 

Country A: Strict regulation 

Country A: Strict regulation 

Country B: Strict regulation

($20B, $20B)

Country B: Light regulation

(–$30B, $45B)

 

Country A: Light regulation

Country A: Light regulation

Country B: Strict regulation

($45B, –$30B)

Country B: Light regulation

($0B, $0B)

Table 3: Illustrative example - cross-border banking regulation

When both countries impose strict regulations, they both benefit from more stable capital inflows. Alternatively, if one country opts for a different regulatory approach, the stricter one tends to experience a decline in capital inflows, as the more lenient country attracts greater activity and opens the door to regulatory arbitrage. However, if both choose to loosen their regulation, neither gains a surplus in capital, and conditions remain flat.

Foreign exchange market intervention

Payoff matrices can help map out the potential outcomes of currency management policies across global markets, especially when it comes to aligning exchange rate regimes with investor expectations. When currencies are allowed to float (particularly in a coordinated manner), it tends to enhance market transparency and signals a country’s confidence in its market mechanisms and domestic policies. On the other hand, uncoordinated efforts to fix currencies can distort pricing signals and increase market volatility.9

Below is a simplified illustration of two hypothetical countries (A and B) deciding whether to intervene in the foreign exchange market or allow their currencies to float, with outcomes measured in billions of dollars ($) of capital.

 

 

B: Intervene

B: Intervene

B: Let float

B: Let float

 

A: Intervene

A: Intervene

B: Intervene

($0B, $0B)

B: Let float

(-$10B, +$10B)

 

A: Let float

A: Let float

B: Intervene

(+$10B, -$10B)

B: Let float

(+$25B, +$25B)

Table 4: Illustrative example - foreign exchange intervention

When both countries decide to intervene, they may succeed in controlling fluctuations in the short term, but it’s the market’s perception of an overarching volatility that keeps net capital flows unchanged. On the other hand, if one country allows its currency to float while the other intervenes, the floater tends to benefit from greater transparency and stronger capital inflows, while the intervening country risks losing attractiveness due to a less favorable exchange rate. Finally, when both countries let their currencies float, mutual credibility can boost market efficiency, global capital mobility, and the perception of long-term stability, which results in capital gains for both.

A fundamentally powerful table

In an increasingly interdependent global economy, strategic decisions made by policymakers, central banks, and institutions rarely occur in isolation. The payoff matrix, while seemingly simple, continues to serve as a powerful tool for mapping outcomes, anticipating interplays between actors, and guiding more informed economic strategies. From interest rate coordination to regulatory standards and currency management, its relevance in macroeconomics remains strong, offering a clearer lens through which to navigate complexity, assess trade-offs, and shape sustainable, forward-looking policy decisions.

 

References

  1. Pilkington A. Topic 15: Two Person Games [Internet]. Notre Dame; 2015 [cited 2025 Jun 23]. Available from:https://www3.nd.edu/~apilking/math10170/information/Lectures%202015/Topic%2015%20Two%20Person%20Games.pdf
  2. Payoff Matrix [Internet]. Xplaind; [cited 2025 Jun 23]. Available from:https://xplaind.com/953905/payoff-matrix
  3. Myerson RB. Game Theory: Analysis of Conflict. Cambridge (MA): Harvard University Press; 1997. 600 p. ISBN: 9780674341166.
  4. Schelling TC. The Strategy of Conflict. Cambridge (MA): Harvard University Press; 1981. 328 p. ISBN: 9780674840317.
  5. Minesso MF, Pagliari MS. DSGE Nash: Solving Nash Games in Macro Models [Preprint]. J Econ Dyn Control. 2024 Dec 17 [cited 2025 Jun 24]. Available from:https://ssrn.com/abstract=5041558
  6. Mohan R, Kapur M. Monetary policy coordination and the role of central banks [Internet]. IMF Working Paper No. 14/70. Washington (DC): International Monetary Fund; 2014 Apr [cited 2025 Jun 24]. Available from:https://www.imf.org/external/pubs/ft/wp/2014/wp1470.pdf
  7. Board of Governors of the Federal Reserve System. Why do interest rates matter? [Internet]. Washington (DC): Federal Reserve; [updated 2023 Nov 15; cited 2025 Jun 24]. Available from:https://www.federalreserve.gov/faqs/why-do-interest-rates-matter.htm
  8. International Monetary Fund, Monetary and Capital Markets Department. Chapter 2. Regulatory reform 10 years after the global financial crisis: looking back, looking forward. In: Global financial stability report, October 2018 [Internet]. Washington (DC): International Monetary Fund; 2018 [cited 2025 Jun 24]. Available from: https://www.elibrary.imf.org/display/book/9781484375594/ch002.xml
  9. Basu S, Das S, Harrison O, Nier E. When foreign exchange intervention can best help countries navigate shocks [Internet]. IMF Blog; 2024 Oct 10 [cited 2025 Jun 24]. Available from:https://www.imf.org/en/Blogs/Articles/2024/10/10/when-foreign-exchange-intervention-can-best-help-countries-navigate-shocks