Learn how to use game theory to design incentives and contracts in various contexts. Discover the differences and trade-offs between repeated and sequential games.

In contexts like contract design or incentive structures, game theory's Subgame Perfect Equilibrium is crucial. For instance, in performance-based contracts for sales teams, stages represent monthly or quarterly targets. Each stage's incentive aligns with broader goals, ensuring strategies remain optimal: Multi-Stage Decisions: Ensures each incentive stage in a contract supports the final objective. Backward Induction: Start from the annual goal and design incentives backward to guarantee each stage motivates effectively. This approach prevents any non-credible threats or promises, maintaining motivation and consistency throughout the contract period.

Repeated games are powerful tools for promoting cooperation, building trust, and ensuring long-term partnerships. By aligning incentives with long-term benefits, they discourage opportunism and create environments where cooperation is not only rational but also rewarding. Repeated negotiations between companies encourage fair terms and compromise, knowing that a hard stance today could sour future deals. Long-term contracts with suppliers often include clauses that reward reliability and penalize delays, ensuring consistent quality and delivery. Anticipating future interactions, players choose cooperation to avoid retaliatory defection in subsequent rounds, leading to a stable cooperative equilibrium.

Last updated on Aug 24, 2024

How can you use repeated and sequential games to design incentives and contracts in various contexts?

Game theory is the study of strategic interactions among rational agents. It can help you understand how to design incentives and contracts in various contexts, such as business, politics, law, and social dilemmas. In this article, we will focus on two types of games that are especially relevant for these purposes: repeated and sequential games.

1 Repeated games

A repeated game is a game that is played multiple times by the same players, with the possibility of changing their actions based on the previous outcomes. Repeated games can create opportunities for cooperation, trust, and reputation, as well as threats of punishment, retaliation, and deterrence. For example, in a repeated prisoner's dilemma, where two suspects can either confess or remain silent, they can achieve a better outcome by cooperating and staying silent, as long as they expect to interact again in the future and value the future payoffs enough. Repeated games can also be used to design incentives and contracts that reward good performance, discourage cheating, and induce long-term relationships.

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Daniel Zaldana

💡LinkedIn Top Voice in Artificial Intelligence | Algorithms | Thought Leadership
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Repeated games are powerful tools for promoting cooperation, building trust, and ensuring long-term partnerships. By aligning incentives with long-term benefits, they discourage opportunism and create environments where cooperation is not only rational but also rewarding. Repeated negotiations between companies encourage fair terms and compromise, knowing that a hard stance today could sour future deals. Long-term contracts with suppliers often include clauses that reward reliability and penalize delays, ensuring consistent quality and delivery. Anticipating future interactions, players choose cooperation to avoid retaliatory defection in subsequent rounds, leading to a stable cooperative equilibrium.

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2 Sequential games

A sequential game is a game where the players move one after another, rather than simultaneously, and have some information about the previous actions. Sequential games can involve strategic foresight, commitment, and credibility, as well as signaling, screening, and bargaining. For example, in a sequential game of chicken, where two drivers can either swerve or continue straight, the first mover has an advantage, as he can commit to a risky action and force the other to yield. Sequential games can also be used to design incentives and contracts that elicit information, reveal preferences, and allocate risks.

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3 Subgame perfect equilibrium

One of the main concepts in game theory is the Nash equilibrium, which is a set of actions that no player has an incentive to deviate from, given the actions of the others. However, in some games, especially sequential games, there may be multiple Nash equilibria, some of which are not credible or consistent. To solve this problem, game theorists use the concept of subgame perfect equilibrium, which is a Nash equilibrium that is also optimal in every subgame of the original game. A subgame is a part of the game that starts after some actions have been taken and ends with the final payoffs. A subgame perfect equilibrium can be found by using the backward induction method, which involves reasoning from the end of the game to the beginning.

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Robert I.

Sales and Marketing Leader | Go-to-Market Strategy | Specializing in eCommerce and Omnichannel | ex-Chobani | Angel Investor
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In contexts like contract design or incentive structures, game theory's Subgame Perfect Equilibrium is crucial. For instance, in performance-based contracts for sales teams, stages represent monthly or quarterly targets. Each stage's incentive aligns with broader goals, ensuring strategies remain optimal: Multi-Stage Decisions: Ensures each incentive stage in a contract supports the final objective. Backward Induction: Start from the annual goal and design incentives backward to guarantee each stage motivates effectively. This approach prevents any non-credible threats or promises, maintaining motivation and consistency throughout the contract period.

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4 Repeated vs sequential games

Repeated and sequential games are both important types of games that can capture different aspects of strategic interactions. However, they also have some differences and trade-offs. Repeated games can allow for more flexibility and adaptation, as the players can adjust their actions based on the history of the game. Sequential games can allow for more commitment and credibility, as the players can influence the expectations and beliefs of the others by moving first or making irreversible choices. Repeated games can also generate multiple equilibria, some of which may be inefficient or unstable. Sequential games can also generate unique equilibria, some of which may be unfair or undesirable.

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5 Applications and examples

Repeated and sequential games can be applied to various contexts and scenarios where incentives and contracts are involved, such as in business, politics, law, or social dilemmas. For instance, in the business sector, firms can use these games to compete or cooperate in the market, design pricing or advertising strategies, negotiate contracts with suppliers or customers, or manage trust. In politics, governments or parties can use them to formulate policies, bargain with other countries or organizations, or signal their intentions. In law, lawyers or judges can use them to argue cases, enforce laws or contracts, bargain settlements or plea deals. Lastly, in social dilemmas, individuals or groups can use them to cooperate or defect in public goods problems, reward or punish others for their actions.

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6 Here’s what else to consider

This is a space to share examples, stories, or insights that don’t fit into any of the previous sections. What else would you like to add?

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How can you use repeated and sequential games to design incentives and contracts in various contexts?

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1 Repeated games

2 Sequential games

3 Subgame perfect equilibrium

4 Repeated vs sequential games

5 Applications and examples

6 Here’s what else to consider

Game Theory

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