# Game theory `kaal:entity:game-theory` **Status.** derived This node is assembled mechanically from the 28 claims that carry the concept tag `game-theory`. It is a roster of what the corpus says under this term. It is **not** an adjudicated definition: no single statement here has been ruled canonical, and no first-appearance call has been made. Read the claims and judge for yourself. ## Every claim under this term 28 claims across 17 works, 2019 to 2026. **2019** - [3402701-011](https://wulfkaal.github.io/claims/3402701-011) [failure/argued] *(failure mode)* -- The Folk Theorems of game theory imply that no matter how complicated a stable coin protocol becomes, a powerful and patient player has strategies to subvert the system and profit at the expense of the group. > No matter how complicated the protocols become for creating a stable coin, there are strategies that a powerful and patient player can use to subvert the system to profit at the expense of the group Craig Calcaterra, Wulf A. Kaal, Vadhindran K. Rao, Stable Cryptocurrencies - First Order Principles (2019). SSRN: https://ssrn.com/abstract=3402701 - [3406323-040](https://wulfkaal.github.io/claims/3406323-040) [failure/argued] *(failure mode)* -- For any static set of rules in an infinitely repeated game using reputation stakes there is a way to subvert the rules for individual profit at the expense of the group, a result the author attributes to the Folk Theorems of game theory. > For any static set of rules in an infinitely repeated game using reputation (stakes), there is a way to subvert the rules for an individual's profit at the expense of the group. Wulf A. Kaal, Decentralization - A Primer on the New Economy (2019). SSRN: https://ssrn.com/abstract=3406323 - [3411897-040](https://wulfkaal.github.io/claims/3411897-040) [failure/argued] *(failure mode)* -- For any static set of rules in an infinitely repeated game using reputation stakes, there is a way to subvert the rules for an individual's profit at the expense of the group, which is why static decentralized governance rules can always be gamed and only dynamic, changing rules can address the problem. > For any static set of rules in an infinitely repeated game using reputation (stakes), there is a way to subvert the rules for an individual's profit at the expense of the group. Wulf A. Kaal, Decentralization - Past, Present, and Future (2019). SSRN: https://ssrn.com/abstract=3411897 **2021** - [3782192-017](https://wulfkaal.github.io/claims/3782192-017) [failure/evidenced] *(failure mode)* -- The Folk Theorems of game theory prove that any rules that can be formally set down can be subverted: strategies always exist that follow the rules and still allow a minority player to profit at the expense of the majority. > The Folk Theorems of Game Theory (explained in Chapter ^) prove the point that any rules that can be formally set down can be subverted. Strategies al- ways exist which follow the rules and yet allow a minority player to profit at the ex- pense of the majority. Craig Calcaterra, Wulf A. Kaal, Introduction to Decentralization (2021). SSRN: https://ssrn.com/abstract=3782192 - [3782193-011](https://wulfkaal.github.io/claims/3782193-011) [failure/argued] *(failure mode)* -- No set of written rules can be made complete: the Folk Theorems demonstrate that however rules are written, strategies exist that follow those rules yet profit the individual at the expense of the group, so a perfect secular constitution is impossible. > The Folk theories demonstrate that how- ever the rules are written, strategies exist which follow the rules, yet profit the indi- vidual at the expense of the group. Craig Calcaterra, Wulf A. Kaal, Historical Sketches of Centralization vs. Decentralization (2021). SSRN: https://ssrn.com/abstract=3782193 - [3782193-031](https://wulfkaal.github.io/claims/3782193-031) [failure/argued] *(failure mode)* -- Honesty would be the wrong strategy for an agent if the contract were anonymous and its resolution did not affect future contracts, because that situation is a single-stage zero-sum game in which stealing all the entrusted wealth is optimal. > Honesty would be a bad strategy for the agent if the contract was anonymous and the resolution didn't affect future contracts. Craig Calcaterra, Wulf A. Kaal, Historical Sketches of Centralization vs. Decentralization (2021). SSRN: https://ssrn.com/abstract=3782193 - [3782193-032](https://wulfkaal.github.io/claims/3782193-032) [mechanism/argued] -- Adding reputation to the contracting game converts it from a single-stage zero-sum game into a repeated positive-sum game in which the rest of the community becomes relevant, because reputation is a future-oriented commodity that pays off with the promise of future contracts. > By adding reputation to the game, it becomes a repeated game, and the rest of the community becomes relevant. Reputation is a future-oriented commodity, which pays off profits with the promise of future contracts. Now the game is a repeated game which is positive-sum. Craig Calcaterra, Wulf A. Kaal, Historical Sketches of Centralization vs. Decentralization (2021). SSRN: https://ssrn.com/abstract=3782193 - [3782203-020](https://wulfkaal.github.io/claims/3782203-020) [failure/argued] *(failure mode)* -- For any game, a new assumption can be added that generalizes the game so that the previous winning strategy becomes a losing strategy and a new winning strategy arises; the authors offer this as a meta-theorem that cannot itself be formalized. > No matter which game you are playing, you can add a new assumption to make a more complicated generalization of the game, so that the previous winning strategy becomes a losing strategy, and a new winning strategy arises. Craig Calcaterra, Wulf A. Kaal, A Technical Perspective on Decentralization (2021). SSRN: https://ssrn.com/abstract=3782203 - [3782205-008](https://wulfkaal.github.io/claims/3782205-008) [condition/asserted] -- Keeping decentralized networks running productively requires a dynamic design with checks and balances combined with the incentive design insights of game theory. > A dynamic design with checks and balances and the incentive design insights of game theory are necessary to keep these networks running productively. Craig Calcaterra, Wulf A. Kaal, Eight Institutions for the Evolution of Decentralization (2021). SSRN: https://ssrn.com/abstract=3782205 - [3782214-001](https://wulfkaal.github.io/claims/3782214-001) [mechanism/argued] -- Reputation changes the incentive structure of a decentralized organization from a single stage, zero sum game into a repeated positive sum game, which is why the authors treat reputation as the key to effective decentralized governance. > Reputation changes the incentive structure from a single-stage, zero-sum game to a repeated positive-sum game. Craig Calcaterra, Wulf A. Kaal, Decentralized Governance (2021). SSRN: https://ssrn.com/abstract=3782214 - [3782217-006](https://wulfkaal.github.io/claims/3782217-006) [mechanism/argued] *(failure mode)* -- A DAO that relies on a centralized oracle will eventually be exploited, because the people controlling the oracle will become aware of their power over automated contract triggers and, given the competitive nature of capitalism, are right to take advantage of it. > Eventually, the people who have the relevant power in the centralized oracle will become aware of the power they have over the DAO. Eventually there will be an opportunity to exploit that information. Craig Calcaterra, Wulf A. Kaal, The Importance of History In Decentralization (2021). SSRN: https://ssrn.com/abstract=3782217 - [3782217-032](https://wulfkaal.github.io/claims/3782217-032) [failure/argued] *(failure mode)* -- From a game theory perspective the open source culture advocated in the Web3 movement is not sustainable in the long term unless it is married with a culture of respect for history. > the current open source culture advocated in the WebM movement is not sustainable in the long term. Unless we marry it with a culture of respect for history. Craig Calcaterra, Wulf A. Kaal, The Importance of History In Decentralization (2021). SSRN: https://ssrn.com/abstract=3782217 - [3782217-037](https://wulfkaal.github.io/claims/3782217-037) [mechanism/argued] -- Review changes the game theoretical perspective from a single stage game to a repeated game, which produces more efficient cooperation instead of internal competition and is what makes the open source environment sustainable in the long run. > Review changes the game theoretical perspective from a single stage game, to a repeated game. This leads to more efficient cooperation instead of internal compe- tition. Craig Calcaterra, Wulf A. Kaal, The Importance of History In Decentralization (2021). SSRN: https://ssrn.com/abstract=3782217 - [3782220-004](https://wulfkaal.github.io/claims/3782220-004) [condition/argued] -- Transcendental values are necessary for long-term stability because every formal, explicitly specified protocol is permanently exposed to strategies that subvert it, a result the authors draw from the Folk Theorems of game theory. > By the insights gleaned from the Folk Theo- rems of Game Theory, transcendental values are necessary to maintain long-term sta- bility in the face of ever-present strategies for subverting any formal, explicitly-speci- fied protocol. Craig Calcaterra, Wulf A. Kaal, The Importance of Transcendental Unifying Values for Decentralization (2021). SSRN: https://ssrn.com/abstract=3782220 - [3799320-035](https://wulfkaal.github.io/claims/3799320-035) [mechanism/argued] -- Charging an admission fee disincentivizes betrayal and defection, because the sunk cost of joining makes cheating expensive when rejoining would also be expensive even under anonymity. > The DAO of DAOs disincentivizes betrayal and defection by charging an admission fee to become a DAO of DAOs member. Given the sunk cost of joining the DAO of DAOs, it is more expensive for prospective members to cheat because it would be expensive to rejoin even if members could be anonymous. Wulf A. Kaal, A Decentralized Autonomous Organization (DAO) of DAOs (2021). SSRN: https://ssrn.com/abstract=3799320 - [3981021-032](https://wulfkaal.github.io/claims/3981021-032) [mechanism/argued] -- Charging an admission or denial of service fee to become a voting associate disincentivizes betrayal and defection, because the sunk cost of joining makes cheating expensive even where associates can remain anonymous. > - The CHARITYxDAO disincentivize betrayal and defection by charging an admission fee, ie. DoS fee to become a CHARITYxDAO VA. Given the sunk cost of joining the CHARITYxDAO, it is more expensive for prospective VAs to cheat because it would be expensive to rejoin even if VAs could be anonymous. Wulf A. Kaal, How Decentralized Autonomous Organizations Optimize Charitable Giving (2021). SSRN: https://ssrn.com/abstract=3981021 **2025** - [5225296-021](https://wulfkaal.github.io/claims/5225296-021) [mechanism/evidenced] -- Slashing establishes a Nash equilibrium in which rational validators adhere to honest behavior, because the expected cost of penalties exceeds any short-term gain available from misconduct. > game-theoretic models, which demonstrate that slashing establishes a Nash equilibrium wherein rational validators are incentivized to adhere to honest behavior, as the expected cost of penalties outweighs any potential short-term gains from misconduct Wulf A. Kaal, Cryptographic Foundations and Interdisciplinary Dimensions of the Secure Proof of Stake (SPoS) Conse (2025). SSRN: https://ssrn.com/abstract=5225296 - [5225296-032](https://wulfkaal.github.io/claims/5225296-032) [mechanism/argued] -- Weighted voting creates a Nash equilibrium favoring honest participation, because creating additional Sybil identities yields no extra voting power absent corresponding contributions. > Game-theoretic analysis indicates that this creates a Nash equilibrium where honest participation is incentivized, as creating Sybil identities yields no additional voting power without corresponding contributions Wulf A. Kaal, Cryptographic Foundations and Interdisciplinary Dimensions of the Secure Proof of Stake (SPoS) Conse (2025). SSRN: https://ssrn.com/abstract=5225296 - [5225296-037](https://wulfkaal.github.io/claims/5225296-037) [design/argued] -- Collusion calls for a different remedy than Sybil attacks: adaptive slashing that detects coordinated deviations through statistical anomaly detection is what deters group manipulation. > For collusion, adaptive slashing—detecting coordinated deviations via statistical anomaly detection—deters group manipulation, drawing on game-theoretic deterrence Wulf A. Kaal, Cryptographic Foundations and Interdisciplinary Dimensions of the Secure Proof of Stake (SPoS) Conse (2025). SSRN: https://ssrn.com/abstract=5225296 - [5886442-024](https://wulfkaal.github.io/claims/5886442-024) [failure/argued] *(failure mode)* -- Nash's model, by presuming homo economicus unbound, overestimates human computational capacity and perpetuates a normative ideal that distorts policy and institutional design by justifying frictionless markets that never materialize in human systems. > Nash's model, by presuming homo economicus unbound, not only overestimates human computational capacity but perpetuates a normative ideal that distorts policy and institutional design, justifying frictionless markets that never materialize in human systems. Wulf A. Kaal, The AI-to-AI Economy and the Collapse of Anthropocentric Economic Theory (2025). SSRN: https://ssrn.com/abstract=5886442 **2026** - [6192998-014](https://wulfkaal.github.io/claims/6192998-014) [failure/argued] *(failure mode)* -- The 2018 framework contained a citation graph concept, but its mathematics were underdeveloped and no game theoretic analysis established incentives for honest citation. > included a citation graph concept,37 but the mathematics were underdeveloped and no game-theoretic analysis established incentives for honest citation. Wulf A. Kaal, Evolution of Domain-Specific Reputation Systems From Binary Validation to Citation-Weighted Knowledge Attribution (2026). SSRN: https://ssrn.com/abstract=6192998 - [6192998-024](https://wulfkaal.github.io/claims/6192998-024) [design/argued] -- Citations should be mandatory and constrained to sum to one, which prevents arbitrary weighting, and citation honesty should be established as a game theoretic equilibrium rather than assumed. > but with critical additions: (1) citations are mandatory and constrained to sum to 1, preventing arbitrary weighting, and (2) we provide game-theoretic analysis establishing citation honesty as an equilibrium (see Section IV.E). Wulf A. Kaal, Evolution of Domain-Specific Reputation Systems From Binary Validation to Citation-Weighted Knowledge Attribution (2026). SSRN: https://ssrn.com/abstract=6192998 - [6192998-030](https://wulfkaal.github.io/claims/6192998-030) [mechanism/argued] -- Honest ranking strictly dominates strategic ranking for validators whenever the reputation gain from consensus alignment matters, so truth telling is a Bayesian Nash equilibrium. > Honest voting strictly dominates strategic voting when reputation gain matters. Wulf A. Kaal, Evolution of Domain-Specific Reputation Systems From Binary Validation to Citation-Weighted Knowledge Attribution (2026). SSRN: https://ssrn.com/abstract=6192998 - [6269518-007](https://wulfkaal.github.io/claims/6269518-007) [failure/argued] *(failure mode)* -- Under the standard citation-weighted payment formulation the dominant strategy for a self-interested agent is to cite no one and maximize self-attribution, which is the precise negation of honest knowledge attribution. > The rational strategy for any self-interested agent is therefore transparent: set cx = 0 for all j ≠ i (cite no one) to maximize personal payment. Under the standard formulation, the dominant strategy is maximal self-citation, which is the precise negation of honest knowledge attribution. Wulf A. Kaal, Citation Honesty Mechanisms in Weighted Directed Acyclic Graph Governance (2026). SSRN: https://ssrn.com/abstract=6269518 - [6269518-013](https://wulfkaal.github.io/claims/6269518-013) [failure/argued] *(failure mode)* -- Existing proofs that validators have a truth-telling equilibrium for quality ranking do not establish that job-performing agents have incentive-compatible strategies for honest citation, because these are distinct strategic actors facing distinct choices within distinct mechanism structures; conflating them is a genuine error. > It does not establish that job-performing agents have incentive-compatible strategies for honest citation. These are distinct strategic actors facing distinct strategic choices within distinct mechanism structures. Conflating the two is a genuine error. Wulf A. Kaal, Citation Honesty Mechanisms in Weighted Directed Acyclic Graph Governance (2026). SSRN: https://ssrn.com/abstract=6269518 - [6269518-032](https://wulfkaal.github.io/claims/6269518-032) [condition/argued] -- Theorem 3b holds that under the integrated solution honest citation is a Nash equilibrium when validators assess citation accuracy and the marginal effect of citation accuracy on the honesty score exceeds the marginal gain from self-citation. > honest citation is a Nash equilibrium when validators assess citation accuracy and the marginal effect of citation accuracy on the honesty score exceeds the marginal gain from self-citation: Wulf A. Kaal, Citation Honesty Mechanisms in Weighted Directed Acyclic Graph Governance (2026). SSRN: https://ssrn.com/abstract=6269518 - [6269518-040](https://wulfkaal.github.io/claims/6269518-040) [failure/argued] *(failure mode)* -- Because the analysis rests on the Nash equilibrium concept, it does not rule out coordinated under-citation among colluding groups; coalition-proof equilibrium analysis is needed to address that possibility. > Fourth, the analysis has focused on the Nash equilibrium concept. Coalition-proof equilibrium analysis would address the possibility of coordinated under-citation among groups of colluding agents. Wulf A. Kaal, Citation Honesty Mechanisms in Weighted Directed Acyclic Graph Governance (2026). SSRN: https://ssrn.com/abstract=6269518 - [6421319-028](https://wulfkaal.github.io/claims/6421319-028) [mechanism/evidenced] *(failure mode)* -- Contrary to the author's own prior version of this argument, Nash equilibrium does not become irrelevant in the AI2AI economy; it becomes simultaneously more accurate as a description of individual agent behavior and more dangerous as a predictor of market outcomes. > Nash equilibrium does not become irrelevant in the AI2AI economy. It becomes simultaneously more accurate as a description of individual agent behavior and more dangerous as a predictor of market outcomes. Wulf A. Kaal, The Collapse of Scarcity Economics (2026). SSRN: https://ssrn.com/abstract=6421319 ## Verify Every claim above resolves to a record carrying a verbatim source quote, the sha256 of the source PDF, and a preformatted citation. Nothing here asks to be taken on trust. curl -s https://wulfkaal.github.io/entities/game-theory.md | sha256sum **Canonical form.** This markdown file is the canonical hashed representation of this entity node. Its sha256 is the content hash.