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Opportunity-Cost-Driven Reward Mechanisms for Crowd-Sourced Computing Platforms

Shuhao Zheng, Ziyue Xin, Zonglun Li, Xue Liu

TL;DR

This work addresses incentive design for crowd-sourced computing where miners may divert power to alternatives due to opportunity costs. It models a repeated decision process with transcripts following a Gamma distribution and defines $OCD-IC$ and $DOCD-IC$ alongside long-term budget balance. The analysis shows traditional PPS can balance budgets per round under assumptions but fails $DOCD$-IC (and sometimes $OCD$-IC) in general, motivating a Pay-Per-Share with Subsidy ($PPSS$) mechanism. PPSS introduces subsidies informed by miners’ capacities and history, achieving $OCD-IC$ and long-term budget balance, with $DOCD$-IC attainable under dynamic conditions, thus offering a more robust and applicable reward framework for real-world crowd-sourced platforms.

Abstract

This paper introduces a game-theoretic model tailored for reward distribution on crowd-sourced computing platforms. It explores a repeated game framework where miners, as computation providers, decide their computation power contribution in each round, guided by the platform's designed reward distribution mechanism. The reward for each miner in every round is based on the platform's randomized task payments and the miners' computation transcripts. Specifically, it defines Opportunity-Cost-Driven Incentive Compatibility (OCD-IC) and Dynamic OCD-IC (DOCD-IC) for scenarios where strategic miners might allocate some computation power to more profitable activities, such as Bitcoin mining. The platform must also achieve Budget Balance (BB), aiming for a non-negative total income over the long term. This paper demonstrates that traditional Pay-Per-Share (PPS) reward schemes require assumptions about task demand and miners' opportunity costs to ensure OCD-IC and BB, yet they fail to satisfy DOCD-IC. The paper then introduces Pay-Per-Share with Subsidy (PPSS), a new reward mechanism that allows the platform to provide subsidies to miners, thus eliminating the need for assumptions on opportunity cost to achieve OCD-IC, DOCD-IC, and long-term BB.

Opportunity-Cost-Driven Reward Mechanisms for Crowd-Sourced Computing Platforms

TL;DR

This work addresses incentive design for crowd-sourced computing where miners may divert power to alternatives due to opportunity costs. It models a repeated decision process with transcripts following a Gamma distribution and defines and alongside long-term budget balance. The analysis shows traditional PPS can balance budgets per round under assumptions but fails -IC (and sometimes -IC) in general, motivating a Pay-Per-Share with Subsidy () mechanism. PPSS introduces subsidies informed by miners’ capacities and history, achieving and long-term budget balance, with -IC attainable under dynamic conditions, thus offering a more robust and applicable reward framework for real-world crowd-sourced platforms.

Abstract

This paper introduces a game-theoretic model tailored for reward distribution on crowd-sourced computing platforms. It explores a repeated game framework where miners, as computation providers, decide their computation power contribution in each round, guided by the platform's designed reward distribution mechanism. The reward for each miner in every round is based on the platform's randomized task payments and the miners' computation transcripts. Specifically, it defines Opportunity-Cost-Driven Incentive Compatibility (OCD-IC) and Dynamic OCD-IC (DOCD-IC) for scenarios where strategic miners might allocate some computation power to more profitable activities, such as Bitcoin mining. The platform must also achieve Budget Balance (BB), aiming for a non-negative total income over the long term. This paper demonstrates that traditional Pay-Per-Share (PPS) reward schemes require assumptions about task demand and miners' opportunity costs to ensure OCD-IC and BB, yet they fail to satisfy DOCD-IC. The paper then introduces Pay-Per-Share with Subsidy (PPSS), a new reward mechanism that allows the platform to provide subsidies to miners, thus eliminating the need for assumptions on opportunity cost to achieve OCD-IC, DOCD-IC, and long-term BB.

Paper Structure

This paper contains 10 sections, 14 theorems, 26 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Our Results
  3. Related Work
  4. Preliminaries
  5. The Model
  6. Reward Function Desiderata
  7. Pay-Per-Share Reward Mechanism
  8. Pay-Per-Share with Subsidy reward mechanism
  9. Conclusion
  10. Proofs of Theorems

Key Result

Theorem 1

The Pay-Per-Share (PPS) reward mechanism $R^{PPS}$ maintains a $\left(0,\frac{b}{p}\right)$-budget balance for each individual round $j$, and by extension, PPS mechanism satisfying $\left(0,\frac{b}{p}\right)$-long term budget balance.

Figures (1)

  • Figure 1: Change in subsidy factor ($K_i$) as a function of total computing power ($A_i$) with parameters $\lambda = 0.8$, $k = 2$ when the completed difficulty $D = 10$.

Theorems & Definitions (28)

  • Example 1
  • Example 2
  • Definition 1: Budget Balanced
  • Definition 2: long-term Budget Balanced
  • Definition 3: Opportunity-Cost-Driven Incentive Compatible
  • Definition 4: Dynamic OCD-IC
  • Theorem 1
  • Theorem 2
  • Theorem 3
  • Theorem 4
  • ...and 18 more