Institutional Game Theory – On-chain Evolution of the (3,3) Paradigm

1. Institutions Are Not Utopias, but Rational Responses to Game Theoretic Reality

Olympus Pact is not founded on utopian idealism, but on the game-theoretic reality of decentralized systems. In a world without central authority, consensus is not a slogan — it is the product of incentives, governance, and trust working in concert.

An institution is a structured alignment of interests and trust. Consensus emerges from the equilibrium of countless self-interested participants navigating rational decisions. Therefore, only precise and dynamic game-theoretic mechanisms can ensure long-term stability and sustainable evolution within decentralized networks.

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2. From (3,3) to Mechanism Design: Modeling Cooperative Games On-Chain

2.1 The (3,3) Model from OlympusDAO

The origin of the (3,3) concept lies in the OlympusDAO community. It models participant decisions in a payoff matrix:

Player A\B	Stake	No Stake	Sell
Stake	(3,3)	(1,2)	(0,1)
No Stake	(2,1)	(0,0)	(-1,0)
Sell	(1,0)	(0,-1)	(-2,-2)

Interpretation:

• Mutual staking yields maximum system rewards — (3,3) reflects full cooperation.

• Selling causes systemic degradation and losses shared by all.

• Over repeated games, defection increases due to short-term arbitrage incentives, leading to equilibrium decay.

2.2 Olympus Pact: Institutionalizing Game Theory

Olympus Pact upgrades this primitive model by embedding incentives into protocol-level rules, transforming game dynamics from voluntary cooperation into systemic alignment through structured incentives.

Our three-tiered incentive structure:

1) Sovereign Stake Layer (Identity Layer):

• Participants stake $PHI to gain identity credentials.

• Time-weighted staking grants higher protocol trust:

2) Governance Game Layer (Signature Weight Layer):

• Participants vote on protocol proposals.

• Signature weight is calculated by:

Wsig=α⋅Tstake+β⋅NgovW_{sig} = \alpha \cdot T_{stake} + \beta \cdot N_{gov}Wsig​=α⋅Tstake​+β⋅Ngov​

Where:

• TstakeT_{stake}Tstake​: staking duration

• NgovN_{gov}Ngov​: number of governance participations

• α,β\alpha, \betaα,β: protocol-defined coefficients

3) Smart Realization Layer (Profit Layer):

• Yield is distributed via dynamic compounding based on protocol evolution:

Rtotal=R0⋅(1+rf(Wsig))tR_{total} = R_0 \cdot \left(1 + \frac{r}{f(W_{sig})}\right)^tRtotal​=R0​⋅(1+f(Wsig​)r​)t

Where:

• rrr: base reward rate

• f(Wsig)f(W_{sig})f(Wsig​): consensus contribution function

• ttt: staking time

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3. Nested Game Structure: A Multi-layered Evolution Beyond Traditional Models

Olympus Pact implements a three-layer nested game structure:

3.1 Protocol Participation Layer (Macro-Economic Incentive Game)

• Strategies: Stake vs. Redeem vs. Idle

• Objective: Maximize individual compounding while maintaining TVL growth

• Mechanism: Dynamic APY, supply contraction, and expectation-driven participation

3.2 Governance Layer (Reputation & Governance Rights Game)

• Strategies: Participate vs. Abstain

• Key Variables: Reputation score RrepR_{rep}Rrep​, governance activity GscoreG_{score}Gscore​

• Outcome: Proposal execution and protocol trajectory

3.3 Asset Support Layer (RWA Inclusion & Treasury Stability Game)

• Strategies: Vote on which assets enter the treasury

• Factors: Asset volatility, liquidity ratings, on-chain mapping reliability

• Systemic Effect: Stability of protocol reserves, token credibility, issuance rhythm

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4. Driving Dual Optimization: Rational Individuals and Systemic Sustainability

The Olympus Pact consensus game model aims to:

• Align individual rational rewards with system growth:

Ui=max⁡(∑t=1TRi(t)−Ci(t))U_i = \max \left( \sum_{t=1}^T R_i(t) - C_i(t) \right)Ui​=max(t=1∑T​Ri​(t)−Ci​(t))

• Ensure long-term sustainability of the protocol:

lim⁡t→∞ddt(∑i=1nRi(t))≥0\lim_{t \to \infty} \frac{d}{dt} \left( \sum_{i=1}^n R_i(t) \right) \geq 0t→∞lim​dtd​(i=1∑n​Ri​(t))≥0

We strive to ensure that each rational individual decision contributes to the system's macro-level prosperity. This is not merely a win for incentive design but a civilizational leap in the institutionalization of on-chain cooperation.

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5. Beyond the Game: Toward Coordinated Prosperity

We do not seek to eliminate games — we seek to civilize them. The true brilliance of Olympus Pact lies in its ability to align self-interest with collective evolution through dynamic, protocol-driven cooperation.

By institutionalizing trust, incentivizing order, and engineering consensus, Olympus Pact establishes a regenerative, self-governing financial system. Here, every rational move strengthens the protocol. Every contribution is rewarded. Every cycle refines the system.

This is not just an upgrade to DeFi. It is the emergence of on-chain institutional civilization.