Smart Contracts
A Game-Theoretic Analogue of the Coase Theorem: Nash Equilibria, the Folk Theorem, and Pareto Efficiency in Non-Cooperative Games with Contract Formation
By Joseph Mark Haykov
July 10, 2025
Abstract
This paper examines whether Nash equilibria are necessarily Pareto-efficient in non-cooperative games where parties have unfettered trade, complete symmetric information, no counterparty risk, and enforceable contract formation (e.g., via smart contracts). Here, “no strategic uncertainty” means that all parties are fully informed and agreements are perfectly enforceable, ruling out any risk of defection or fraud. While perfect honesty would require “saintly” agents, these conditions can be operationalized through transparent information and credible contracting. We show that, under these assumptions, rational players invariably select Pareto-efficient Nash equilibria. This efficiency results from the credible enforcement of cooperative strategies, as predicted by the Folk Theorem in repeated games. We thus formalize a game-theoretic analogue of the Coase Theorem: when strategic uncertainty is eliminated, efficiency is assured. Examples such as airline scheduling and telecom protocol standardization illustrate the practical relevance. Under these idealized conditions, inefficient Nash equilibria simply cannot persist.
Introduction
The Coase Theorem (Coase, 1960) famously states that when property rights are well-defined, transaction costs are zero, and information is complete, voluntary bargaining will produce Pareto-efficient outcomes in the presence of externalities. In practice, however, these ideal conditions rarely exist: enforcing property rights or contracts can be prohibitively expensive, and incomplete information often prevents efficient negotiation. As a result, real-world systems rely on mechanisms like taxation or regulation to address inefficiencies and align incentives.
This paper investigates a central question in game theory: under what conditions are Nash equilibria necessarily Pareto-efficient? Specifically, we ask whether, in non-cooperative games with unrestricted negotiation, complete symmetric information, no counterparty risk, and enforceable contract formation, inefficiency can ever persist.
We focus on games with three defining features:
Unfettered Trade: Parties can negotiate and form binding contracts freely, without regulatory or transactional barriers.
No Strategic Uncertainty: All players have complete and symmetric information about payoffs, preferences, and available strategies. This rules out any possibility of counterparty risk or defection: all agreements are perfectly enforceable.
Contract Formation as a Strategic Option: Players can strategically propose and enter binding agreements, internalizing externalities or conflicts within the game’s structure.
Our analysis demonstrates that, under these conditions, every Nash equilibrium must be Pareto-efficient. When there is no uncertainty about counterparties’ behavior and all contracts are perfectly enforceable, rational players adopt cooperative strategies that replicate the efficient outcomes predicted by the Folk Theorem. Crucially, this result does not depend on repeated play or reputation; efficiency is guaranteed by the structural elimination of all strategic uncertainty. In this way, we extend the logic of the Coase Theorem beyond bargaining over externalities to the broader context of strategic interaction under perfect information and enforceable contracting.
The Coase Theorem and Economic Efficiency
The Coase Theorem states that when property rights are well-defined, information is complete, and transaction costs are zero, voluntary negotiation will produce Pareto-efficient solutions to externalities. For instance, if a factory’s pollution harms a nearby fishery, both parties can reach an agreement—such as the fishery compensating the factory to reduce emissions—that internalizes the externality and maximizes total surplus. The essential logic of the theorem relies on enforceable agreements and rational bargaining, ensuring mutually beneficial outcomes regardless of how rights are initially allocated.
Game-Theoretic Framework and Strategic Enforcement
We consider a non-cooperative game involving any number of rational, symmetrically informed players, each able to negotiate and enforce binding agreements (contracts). The core elements of this framework are:
Strategies: Each player can choose a standard strategy or a contract strategy. Choosing the contract strategy signals a willingness to enter a binding, enforceable agreement.
Payoffs: Payoffs are modeled on real-world coordination problems—such as airline scheduling or telecom protocol standardization—and reflect both conflicting interests and incentives for cooperation.
Nash Equilibrium: A set of strategies where no player can gain by unilaterally deviating.
Pareto Efficiency: An outcome where no player can be made better off without making at least one other player worse off.
Real-World Illustration: Airline Scheduling
Consider two airlines—Delta and United—that must select scheduling standards to optimize passenger connections. Their interaction is captured in the following payoff matrix (each cell is “(Delta, United)”):
United: Schedule X
United: Schedule Y
United: Contract
Delta: Schedule X
(7, 3)
(0, 0)
(2, 2)
Delta: Schedule Y
(0, 0)
(3, 7)
(2, 2)
Delta: Contract
(2, 2)
(2, 2)
(5, 5)
Rows: Delta’s strategies. Columns: United’s strategies.
Each cell: Payoff tuple (Delta, United).
At first glance, there are three pure-strategy Nash equilibria:
(Schedule X, Schedule X) → (7, 3)
(Schedule Y, Schedule Y) → (3, 7)
(Contract, Contract) → (5, 5)
However, under our assumptions—symmetric information, rationality, and enforceable contract formation—only (Contract, Contract) is viable in practice. The player disadvantaged in (7, 3) or (3, 7) knows a mutually better (5, 5) contract is achievable and has no reason to accept an inferior payoff. The advantaged player, aware of this, cannot expect the other to settle for less.
Thus, (Schedule X, Schedule X) and (Schedule Y, Schedule Y) are not stable when contracts are enforceable and information is symmetric. Rational players will always deviate toward the Pareto-efficient contract outcome, making (5, 5) the unique practical equilibrium.
Strategic Enforcement and the Folk Theorem
Why do rational players always select the Pareto-efficient (5, 5) equilibrium? The answer is enforcement: in repeated games, the Folk Theorem (Fudenberg & Tirole, 1991) shows that mutually beneficial outcomes can be sustained by the credible threat of retaliation—if you cheat, you get punished later.
In our model, repetition isn’t needed. When information is complete, there is no counterparty risk, and contracts are perfectly enforceable, the logic of tit-for-tat becomes credible even in one-shot or finitely repeated games. Players know that any deviation will result in immediate contractual penalties or enforceable retaliation, so cooperation is not just preferred, but structurally required.
In this idealized setting, rational and fully informed players have no incentive to break the contract, as defection strictly reduces their expected payoff. While real-world inefficiencies—like imperfect enforcement or information asymmetry—can undermine this mechanism, our framework isolates the pure logic: eliminate strategic uncertainty, and tit-for-tat enforcement guarantees efficient cooperation, even in static (one-shot) games.
Coase Theorem vs. Folk Theorem
Both the Coase Theorem and the Folk Theorem rest on a shared foundation: rational bargaining, enforceable agreements, complete (and symmetric) information, and baseline mutual trust. When these conditions are met, both predict Pareto-efficient outcomes.
The key difference is context. The Coase Theorem focuses on economic bargaining over externalities, highlighting the role of legal frameworks and costless negotiation. The Folk Theorem, by contrast, explains how cooperation can be sustained in repeated games—enforcement here relies on the threat of future punishment for defection.
Our framework unifies these perspectives by showing that, when strategic uncertainty is eliminated, even one-shot games with enforceable contracts can achieve the same cooperative incentives usually associated with repeated interactions. In short, perfect enforceability substitutes for repetition, making the logic of efficiency common to both the Coase and Folk Theorems.
The logic here is robust: under these specified conditions, inefficient Nash equilibria are simply not credible. Rational, symmetrically informed agents—aware of the superior contract-based payoff—have no incentive to accept or persist in inferior outcomes.
Because deviating from the efficient contract yields strictly lower payoffs, and every player knows this with certainty, each agent can confidently expect others to adhere to the efficient strategy. Inefficient strategies are thus strictly dominated and never chosen in equilibrium.
As a result, the Pareto-efficient outcome is uniquely stable—not just because of coordination, but because rational expectations and enforceability eliminate any incentive to deviate.
Additional Real-World Example: Telecom Protocols
Consider two telecom firms—AT&T and Verizon—facing the choice of coordinating on a new protocol. Protocol X favors AT&T (e.g., prioritizing high bandwidth), while Protocol Y favors Verizon (e.g., optimizing for low latency). Alternatively, the firms can agree to a contract: a mutually beneficial hybrid protocol that balances both interests.
As with the airline scheduling example, the game is symmetric. Each firm has an incentive to avoid one-sided standards in favor of an enforceable agreement that maximizes joint efficiency. When information is complete, counterparty risk is absent, and contracting is enforceable, rational players always select the efficient, contract-based equilibrium.
This example reinforces the core claim: when strategic uncertainty is eliminated, enforceable contracting consistently yields Pareto-efficient outcomes—even in complex, real-world coordination problems.
Conclusion
We have shown that, in non-cooperative games with unfettered negotiation, complete symmetric information, no counterparty risk, and enforceable contracting, Nash equilibria are necessarily Pareto-efficient. This result extends the logic of the Coase Theorem to a broader class of strategic interactions, formalizing an efficiency guarantee when every avenue for opportunistic behavior is operationally closed.
The key mechanism is straightforward: with strategic uncertainty eliminated, tit-for-tat enforcement becomes fully credible—even in one-shot or finitely repeated games. Rational players, knowing that deviation triggers enforceable retaliation, have no incentive to settle for inefficient outcomes. Thus, the absence of strategic uncertainty acts as a functional substitute for reputational discipline, ensuring efficiency in equilibrium.
By combining perfect information, rational agents, and legally enforceable contracts (such as “TNT-Bank” smart contracts), we unify the core insights of the Coase and Folk Theorems—yielding a comprehensive, formal framework for efficiency in non-cooperative settings.
References:
Coase, R. H. (1960). “The Problem of Social Cost.” Journal of Law and Economics, 3, 1–44.
Fudenberg, D., & Tirole, J. (1991). Game Theory. MIT Press.
Abreu, D. (1988). “On the Theory of Infinitely Repeated Games with Discounting.” Econometrica, 56(2), 383–396.
Maskin, E., & Tirole, J. (1999). “Unforeseen Contingencies and Incomplete Contracts.” The Review of Economic Studies, 66(1), 83–114.
Hart, O., & Moore, J. (1999). “Foundations of Incomplete Contracts.” The Review of Economic Studies, 66(1), 115–138.