Promises: On Relationships Between Promises And Decisions

A promise is an interesting tool in decision governance. A promise can be used to make future behavior, including decisions, easier to predict. The outcome of a promise – if it is fulfilled or not – can serve as an input to the evaluation of competence and reputation, both of which influence trust, and in turn, the variety and importance of decision rights we may consider assigning to someone. This text is an overview of how the concept of promise is used in economics.

This text is part of the series on decision governance. Decision Governance is concerned with how to improve the quality of decisions by changing the context, process, data, and tools (including AI) used to make decisions. Understanding decision governance empowers decision makers and decision stakeholders to improve how they make decisions with others. Start with “What is Decision Governance?” and find all texts on decision governance here.

A promise in economics is formalized through models of commitment, contractual enforcement, or strategic signaling. The economic significance of a promise lies in its effect on the expectations and behaviors of others, and in the institutional or strategic mechanisms that make it credible.

Promises as Commitments in Game Theory

In dynamic games, promises are modeled as strategic commitments that influence expectations and future choices. A promise can be formalized as a strategy announcement or a binding commitment to a course of action, which alters the structure of the game or the beliefs of other players. Formal structure (in extensive-form games):

• Let \( G \) be a game with players \( i \in N \), histories \( h \), and strategy sets \( S_i \).
• A promise by player \( I \) is a pre-play communication or move \( m_i \in M_i \) that maps to a strategy \( s_i \in S_i \).
• The promise has value only if it affects beliefs or subsequent actions of other players, and can be credible if backed by a commitment device or reputational concern.

Promises can influence equilibrium outcomes in cheap talk games (Crawford & Sobel, 1982), though they are non-binding unless they are coupled with incentives or penalties.

Promises in Contract Theory

In contract theory, a promise is equivalent to a contractual obligation—a commitment to perform a specified action under defined conditions. Formal structure:

• A contract \( C \) is a tuple \( (a, t) \), where \( a \) is the promised action and \( t \) is the transfer (payment) contingent on \( a \).
• Let \( u_i(a, t) \) be the utility function of agent \( i \), and \( c(a) \) be the cost of action \( a \).
• A promise is enforceable if the incentive compatibility condition holds:
  \(
  u_i(a, t) – c(a) \geq u_i(a’, t’) – c(a’) \quad \forall a’ \in A
  \)
  That is, the agent has no incentive to deviate from the promised action.

In incomplete contract theory (Grossman & Hart, 1986), promises are understood as commitments that may not be fully specified or enforceable ex ante, and relational contracts (Baker, Gibbons, & Murphy, 2002) capture informal promises sustained by repeated interaction and reputational incentives.

Promises as Signals in Mechanism Design

Promises can be modeled as signals of intent or type in mechanisms where information asymmetry exists. A promise may serve to credibly reveal private information if it is costly to fake or can be verified ex post. Formal structure:

• In a signaling game, a sender \( i \) chooses a message \( m \) (a promise) conditional on their type.
• The receiver updates beliefs via Bayes’ rule and chooses an action.
• The promise is credible if it is a separating equilibrium: only types who intend to follow through would find it optimal to make the promise.

Types of senders:

• The sender’s type captures characteristics such as ability, reliability, or preference for cooperation.
• For example, in labor markets, a job candidate (sender) may promise punctuality and reliability. Types might include: “high effort” (likely to follow through) and “low effort” (likely to shirk). Only the high-effort type finds it worthwhile to make and keep such a promise, as reneging imposes reputational or career costs.

This framework is central to models of reputation (Kreps & Wilson, 1982), where the cost of reneging on a promise affects future payoffs.

References

• Crawford, V. P., & Sobel, J. (1982). Strategic Information Transmission. Econometrica, 50(6), 1431–1451.
• Grossman, S. J., & Hart, O. D. (1986). The Costs and Benefits of Ownership: A Theory of Vertical and Lateral Integration. Journal of Political Economy, 94(4), 691–719.
• Baker, G., Gibbons, R., & Murphy, K. J. (2002). Relational Contracts and the Theory of the Firm. Quarterly Journal of Economics, 117(1), 39–84.
• Kreps, D. M., & Wilson, R. (1982). Reputation and Imperfect Information. Journal of Economic Theory, 27(2), 253–279.

Definitions

• Commitment Device: A mechanism that restricts future choices to make a current promise credible (Schelling, 1960).
• Cheap Talk: Costless, non-binding communication between players before a game.
• Relational Contract: Informal agreements sustained by the value of future relationships rather than formal enforcement (Baker et al., 2002).
• Incentive Compatibility: A condition under which each participant’s optimal strategy leads them to act in accordance with the desired outcome.