Liar's Game: Conviction is Everything

Abstract: The Impossibility of Good Faith

What does it require for two individuals to trade information? Traditionally, we enforce this trade with a middleman who oversees the transaction and enforces fairness, ensuring one actor doesn’t cheat the other. But what if we do not want to use a middleman and still guarantee a fair exchange?

The catch to all this is that it has been mathematically proven by Even, Goldreich, and Lempel (1985), and later expanded upon by Richard Cleve (1986) regarding the impossibility of fair exchange without a trusted third party, that it’s strictly not possible. Lol (can’t we all just do better).

The reason it is mathematically impossible is because, if we scrape the surface of what drives any actor, we inevitably move from morality to Utility and Incentives (U & I). How then can two individuals exchange information when they have thrown morality out the window and strictly optimize for U & I?

To solve this, let’s play a game.

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1. The Core Problem Definition

In this game, we have Alice (the Seller) and Bob (the Buyer).

• Alice has a secret and is willing to give it out for a fixed fee.
• Bob wants that secret and is willing to pay for it.

The problem is very simple: how do both parties exchange value fairly? The rules of the game are: there are no rules.

Let’s look at the three base scenarios of this unregulated exchange:

Game 1: The Honest Exchange

Alice gives Bob a secret. Bob verifies that the secret is valid, and Bob gives Alice the fixed fee.

Payout Matrix: Game 1

Actor	Asset Transfer	Final State
Alice (Seller)	- Secret (Valid), + Fixed Fee	Happy
Bob (Buyer)	+ Secret (Valid), - Fixed Fee	Happy

Game 2: The Dishonest Seller

Alice gives Bob a false secret knowingly. Bob verifies the secret, realizes Alice is trying to cheat him, and refuses to pay. Because we aren’t dealing with a middleman, once Alice hands over the secret, Bob cannot hand over the fixed fee until he verifies it. Because Alice’s secret is invalid, they part ways.

Payout Matrix: Game 2

Actor	Asset Transfer	Final State
Alice (Seller)	- Secret (Invalid), + Fixed Fee (0)	Neutral
Bob (Buyer)	+ Secret (Invalid), - Fixed Fee (0)	Neutral

Game 3: The Dishonest Buyer (Our Game of Interest)

Alice gives Bob a valid secret. Bob verifies it and concludes the secret is “invalid” (a lie), intending to cheat Alice out of her fixed fee. To make matters worse, Bob cannot magically “forget” what he just consumed. The power shifts entirely to Bob.

Payout Matrix: Game 3

Actor	Asset Transfer	Final State
Alice (Seller)	- Secret (Valid), + Fixed Fee (0)	Sad
Bob (Buyer)	+ Secret (Valid), - Fixed Fee (0)	Happy

We would like all games to go like Game 1, but that is wishful thinking relying on good faith. How can we enforce that even when Alice and Bob do not intend on playing nice, they have no other choice but to play nice?

To mitigate Game 3, I propose a challenge protocol. If Bob cheats Alice out of a payment, Alice can challenge Bob. If she wins, she gets her fee. If Bob defends his lie, it will cost him more than if he had simply paid the fixed fee.

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2. Protocol Components & Architecture

This protocol heavily penalizes spam disputes and irrational behaviour, driving actors to concede when they are lying.

Variables

• $E(p)$: Payment Escrow — The capital locked by the buyer representing the agreed-upon value of the information.
• $X$: The Escalation Threshold — The maximum rational bounds of the game. $X$ is directly proportional to $E(p)$ via a multiplier (e.g., 10). If $E(p)$ is 100, then the threshold $X$ becomes 1,000. This ensures the escalation does not operate on a strict 1:1 ratio.
• $B(t)$: Truth Bond — The collateral required to initiate or defend a dispute at a given turn.
• $T(n)$: The Current Turn — The sequential step in the escalation game.
• $L(P)$: Liquidity Pool — A decentralized pool where actors can borrow highly leveraged collateral for their Truth Bonds.

Phase 1: Escrow & Evaluation Window

• Bob (Buyer) escrows the payment amount $E(p)$.
• Alice (Seller) transmits the information to Bob.
• The Evaluation Window begins. Bob has a time-locked window to either accept the information (releasing $E(p)$ to Alice) or issue a challenge. (Note: Only the buyer can issue a challenge, as it is part of the decision matrix of receiving goods).
• To issue a challenge, Bob must lock an initial Truth Bond $B(t)$.
• Anti-Ghosting Mechanism: During the evaluation window, ghosting is impossible. If the window elapses and Bob has not taken any action (neither releasing funds nor challenging), the protocol automatically defaults and releases $E(p)$ to Alice regardless of the secret’s validity.

Phase 2: The Escalation Game (Gradual Progression)

If Bob challenges the validity of the secret, the game enters the Escalation Phase.

• Alice must match the truth bond amount to defend her position.
• At each sequential turn $T(n)$, a strict per-turn clock is enforced. Actors must either Hold (1) by funding their respective escalation tier, or Fold (0) by conceding defeat.
• If either Alice or Bob fails to respond or fund their tier within the window, they automatically default and lose.
• Gradual and Progressive Escalation: An actor cannot simply pay 20 to instantly borrow 200 in liquidity and skip tiers to rapidly push the escalation. Instead, the game enforces a strictly gradual and progressive pattern. Each turn requires a calculated, incremental increase in the Truth Bond $B(t)$, forcing both actors to methodically climb toward the threshold $X$.

Phase 3: The Liquidity Pool & Refund Mechanics

To ensure “Whales” cannot simply bankrupt “Shrimps” by escalating until the poorer party runs out of capital, actors utilize a Liquidity Pool.

• Users can borrow collateral heavily leveraged, paying a small fee at each progressive turn to access the liquidity required to match the current $B(t)$.
• Borrowing Limit (Past $X$): Users can continue to borrow liquidity past the threshold $X$. The same put-up-collateral-to-borrow-liquidity mechanic is enforced to ensure actors don’t suddenly fall into a 1:1 raw capital battle even at high stakes.
• The Refund Law: It effectively costs nothing for the honest actor to defend the truth below the threshold. If a challenge concludes before crossing $X$, the winning party’s collateral fees are simply returned to them. The losing party’s collateral fees are sent to the liquidity pool to cover the borrow and compensate the pool.

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3. Edge Cases, Mitigations, and Payout Matrices

Edge Case A: The “Whale vs. Shrimp” Attack (Resource Exhaustion)

Scenario: Bob (Shrimp) sells valid info for $E(p)$ = 100. Therefore, $X$ = 1,000. Alice (Whale) buys it, then initiates a challenge to bankrupt Bob, hoping Bob cannot match Truth Bonds at higher $T(n)$ levels.

Mitigation: Bob utilizes the Liquidity Pool. He does not need massive capital; he only needs to pay small, progressive fees to borrow the required Truth Bond $B(t)$ at each step. Because Alice is mathematically trapped by the progressive climb toward the $X$ threshold, she cannot just jump the queue. She must bleed fees gradually. Against an honest Bob backed by pool liquidity, Alice is forced to concede.

Payout Matrix: Whale vs Shrimp (Alice Concedes Before $X$) Assume Alice slowly escalates until she has posted 200 in cumulative collateral fees before folding. Bob posted 200 in collateral to sequentially match her.

Actor	Asset Transfer	Final State
Alice (Whale, Buyer, Liar)	-100 (Escrow lost to Bob), - 200 (Collateral sent to pool)	Net: -300
Bob (Shrimp, Seller, Honest)	+100 (Escrow won), 0 (His 200 collateral is returned to him)	Net: +100
Liquidity Pool	+200 (Siphoned from Alice’s lost collateral)	Net: +200

Edge Case B: The Irrational Griefing Attack

Scenario: Alice (Seller) provides fake data for $E(p)$ = 100. $X$ = 1,000. Bob (Buyer) is honest and issues a challenge. Alice knows she is lying but decides to escalate gradually to force Bob to pay collateral fees just to protect his own escrow.

They push the escalation progressively until both have posted 90 in cumulative collateral. Alice then backs off. If Bob lost his 90 collateral to protect his 100 escrow, he practically gained nothing.

Mitigation (The Refund Law): Because Alice conceded, Bob is recognized as the truth-teller. Bob’s 90 collateral is returned to him in full. Alice’s 90 collateral is sent to the pool. Bob protects his 100 for free. The protocol ensures that $P=E(p)-E(x)$ (where $E(x)$ is the final cost of escalation) is never detrimental to the honest party, because for the winner below $X$, $E(x)=0$.

Payout Matrix: Griefing Attack (Alice Concedes Before $X$)

Actor	Asset Transfer	Final State
Alice (Seller, Liar)	-90 (Collateral sent to pool)	Net: -90
Bob (Buyer, Honest)	+100 (Escrow returned), 0 (His 90 collateral is returned to him)	Net: +100
Liquidity Pool	+90 (Alice’s lost collateral pays the pool)	Net: +90

Edge Case C: Crossing the Event Horizon (Threshold $X$)

Scenario: What happens when an escalation reaches and crosses the maximum threshold $X$ ? By design, the gradual climb makes sustaining a lie inevitably eclipse the value of the information. If the challenge crosses $X$ (e.g., passing 1,000), we are watching two completely irrational actors at play.

Mitigation: Escalations past $X$ still require collateral to borrow liquidity (preventing a 1:1 capital death match), but the rules of engagement become extremely punitive. At this point, any collateral put up by BOTH parties past the threshold $X$ is sent directly to the pool and is non-refundable, regardless of who wins. Furthermore, the loser’s collateral from before crossing the threshold is also routed to the pool. The winner only gets their pre-threshold collateral returned.

Why pay 105 in collateral for a 100 secret? You end up losing 5 even if you win. If you lose, you lose $E(p)+\text{Pre-}X\text{ Collateral}+\text{Post-}X\text{ Collateral}$. This creates an absolute mathematical deterrent against infinite escalations.

Payout Matrix: Crossing Threshold $X$ Assume $E(p)$ = 100, $X$ = 1,000. Total collateral paid to borrow up to $X$ is 150 each. They push past $X$ by posting an additional 50 in collateral each. Alice finally concedes.

Actor	Asset Transfer	Final State
Alice (Liar)	-100 (Escrow), -150 (Pre-X collateral sent to pool), -50 (Post-X collateral sent to pool)	Net: -300
Bob (Honest)	+100 (Escrow won), 0 (Pre-X collateral returned to him), -50 (Post-X collateral sent to pool)	Net: +50
Liquidity Pool	+150 (Alice’s Pre-X) + 50 (Alice’s Post-X) + 50 (Bob’s Post-X)	Net: +250

(Note: Bob protected his escrow but burned 50 of his own money acting irrationally past $X$. Alice suffered a heavy net loss for pushing a lie past the mathematical boundary).

Edge Case D: Liquidity Pool Manipulation / The Sybil Attack

Scenario: A malicious actor (Alice) attempts to manipulate the system by interacting with the liquidity pool, hoping to game the borrowing mechanics (e.g., secretly funding Bob’s defense through backchannels while conceding on her own end to somehow “steal” the liquidity).

Mitigation: Because we are working strictly with a decentralized Liquidity Pool rather than peer-to-peer individual brokers, this attack vector is structurally neutralized. Borrowed liquidity is never awarded to the opposing player as a prize. The winner simply gets their own collateral returned, while the loser’s collateral is routed directly back to the smart contract pool. There is no individual broker bond for Alice to extract or steal. Playing both sides of an escalation just results in the attacker paying fees directly to the protocol with zero extraction possible.

Payout Matrix: Sybil / Pool Manipulation Attempt Alice tries to fake a dispute and concede to extract pool funds. Escrow $E(p)$ = 100. She posts 50 collateral as Alice, and 50 collateral funding Bob.

Actor	Asset Transfer	Final State
Alice (Playing both sides)	-50 (Lost as the “loser”, sent to pool), 0 (Returned as the “winner”, net zero)	Net: -50
Liquidity Pool	+50 (Siphoned from Alice’s losing side)	Net: +50

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Conclusion

Liar’s Game operates on the premise that honesty can be mathematically enforced when the cost of maintaining a lie scales progressively against the liar. By leveraging a strict turn-based escalation game, a decentralized liquidity pool to protect the resource-constrained, and a zero-sum refund mechanism that makes defending the truth virtually free, we ensure that malicious actors have no financially viable path to victory.