Definition

A protocol is an explicit, shared, constitutive rule set that fixes the strategy space of an object game (its legal moves and their form, meaning, and sequencing) so that interaction requires conformity rather than interpretation, which lowers the cost of coordination among parties without shared history.

It thereby prices admission to the object game: conformity buys interaction with other conformers, non-conformity buys exclusion.

The value of admission is set externally to the protocol by the population of adopters rather than by the authors.

Discretion is not eliminated but relocated from the point of interaction to the points of specification, adoption, and revision.

Where the object game is a coordination game, a protocol is a convention (self-enforcing).
Where the object game is a cooperation game is an accountability structure (deviation is legible) Where the object game is a mechanism design cooperation game, it also prices moves inside the game.

A protocol isn't a game with a winning move. "Conform" has no rival strategy to beat; every other option is a non-move that returns you to before the gate. It's a non-game, a gate with a single legal move, between two games:

1. Adoption game (real game): which protocol, if any, to conform to. Strategies are the candidate protocols plus "none"; payoffs depend on what others choose. This has winning moves (pick the one that wins the standards war) and it's where lock-in lives.
2. Protocol (gate, not game): the entry price fixed by the adoption you made.
   One move: conform.
   Cost: compliance.
   Return: admission.
3. Object game (real game): what you do once admitted, against or with other admitted parties, with payoffs decided outside of this game.

Terms Used In The Definition

• Explicit: articulable in a form that can be followed without the author present; contrasts with tacit practice. Polanyi, The Tacit Dimension (1966). The etymology (protokollon, the glued-on first leaf recording a roll's contents; then diplomatic "protocol" as the written record of agreed procedure) already carries "written, prior, binding". OED s.v. "protocol".
• Constitutive rule: a rule that creates the possibility of the activity rather than regulating a pre-existing one ("X counts as Y in context C"). Searle, Speech Acts (1969), ch. 2; earlier as "practice rules" in Rawls, "Two Concepts of Rules", Philosophical Review 64 (1955).
• Object game / game: a set of players, strategies, and payoffs. von Neumann & Morgenstern, Theory of Games and Economic Behavior (1944). The meta/object layering: Howard, Paradoxes of Rationality: Theory of Metagames and Political Behavior (1971). The looser "language-game" sense of rule-governed practice: Wittgenstein, Philosophical Investigations (1953), §§7, 23, 66ff.
• Strategy space: the set of complete contingent plans available to a player; the protocol fixes this, the world fixes the payoffs over it. Nash, "Non-Cooperative Games", Annals of Mathematics 54 (1951).
• Legal moves — form, meaning, sequencing: the networking triad "syntax, semantics, timing". Tanenbaum & Wetherall, Computer Networks (5th ed. 2011), §1.3. Fuller decomposition (service, assumptions, vocabulary, encoding, procedure rules): Holzmann, Design and Validation of Computer Protocols (1991), ch. 2.
• Conformity rather than interpretation: the point of interaction is designed to need no judgement. The discretion budget that remains is graded and explicit: Bradner, RFC 2119 (1997), MUST/SHOULD/MAY. The counter-principle that reintroduces judgement at the receiving edge: Postel, RFC 761/793 (1980/81), §2.10, "be conservative in what you do, be liberal in what you accept". On why rule-following always has residual discretion at the edges: Hart, The Concept of Law (1961), ch. 7, "open texture".
• Admission / exclusion as the price: conformity's payoff is access to other conformers, so its value rises with adoption. Katz & Shapiro, "Network Externalities, Competition, and Compatibility", American Economic Review 75 (1985); Farrell & Saloner, "Standardization, Compatibility, and Innovation", RAND Journal of Economics 16 (1985). Lock-in and path dependence: David, "Clio and the Economics of QWERTY", AER 75 (1985); Arthur, "Competing Technologies, Increasing Returns, and Lock-In", Economic Journal 99 (1989).
• Endogenous value / self-perpetuating: a protocol persists because adopters keep paying the entry price for each other, independent of the authors. Rao et al., "The Unreasonable Sufficiency of Protocols", Summer of Protocols pilot study (2023) — working-paper status, but the clearest statement of adoption-driven durability.
• Convention / coordination game / self-enforcing: a regularity in behaviour that is a solution to a recurrent coordination problem, sustained because each party expects the others to conform. Lewis, Convention: A Philosophical Study (1969), ch. 1 — this is very nearly a definition of protocol in the fixing sense. Focal points and commitment devices: Schelling, The Strategy of Conflict (1960), chs. 3 and 5.
• Cooperation game: one where unilateral deviation can pay (prisoner's dilemma structure). Axelrod, The Evolution of Cooperation (1984).
• Accountability / legibility of deviation: the protocol makes it possible to prove that a specific party deviated. Haeberlen, Kuznetsov & Druschel, "PeerReview: Practical Accountability for Distributed Systems", SOSP (2007). (Scott's "legibility" in Seeing Like a State (1998) is the sociological cousin but points at the state's reading of subjects, not peers' reading of each other; I'd cite it for flavour, not for the concept.)
• Mechanism (pricing inside the game): a rule set that also specifies payoffs and relies on players' incentives to produce a target outcome. Hurwicz, "On Informationally Decentralized Systems" (1972); Vickrey, "Counterspeculation, Auctions, and Competitive Sealed Tenders", Journal of Finance 16 (1961); Myerson, "Optimal Auction Design", Mathematics of Operations Research 6 (1981). Fusion with protocol: Nakamoto, "Bitcoin: A Peer-to-Peer Electronic Cash System" (2008); Buterin et al., "Combining GHOST and Casper" (2020); Roughgarden, "Transaction Fee Mechanism Design for the Ethereum Blockchain: An Economic Analysis of EIP-1559" (2020).
• Relocated discretion — specification, adoption, revision: the governance layer that sits above the mechanical one. Clark, "A Cloudy Crystal Ball" (IETF 24 plenary, 1992): "rough consensus and running code"; Resnick, RFC 7282, "On Consensus and Humming in the IETF" (2014).

The one substantive commitment here is that "protocol" is a genus (Lewis-convention) with mechanism as a species, rather than the reverse. We will explore the reverse case in the next article.

Value of Admission to an Object Game

The value of admission to an object game decomposes as: expected payoff from the object game, multiplied by the number and quality of counterparties who are also admitted, minus the cost of compliance.

The first term the world sets, the second the adopters set, the third the authors set. The protocol controls only the third and, weakly, the first through what the strategy space allows. So the protocol's authors price entry to the object game, but the adopters decide what entry is worth to them.

Simple form

Where Vi is the value of admission to player i, A is the set of admitted (conforming) players, qj is the quality of counterparty j, meaning the expected payoff to i from playing the object game with j, and ci is the cost to i of complying with the protocol.

Decomposed Form

Where ui(G, j) is the payoff to i from object game G played against j (set by the world), |A| is the population of conformers (set by the adopters), and ci(P) is the compliance cost imposed by protocol P (set by the protocol authors).

Consequences

Adoption condition:

Network effect: Vi is increasing in |A|. The protocol's authors control only ci(P) and, weakly, ui via the strategy space. The adopters control |A| and qj.