An Incentive Mechanism for Federated Learning:A Continuous Zero-Determinant Strategy Approach

As a representative emerging machine learning technique, federated learning(FL) has gained considerable popularity for its special feature of “making data available but not visible”. However, potential problems remain, including privacy breaches, imbalances in payment, and inequitable distribution.These shortcomings let devices reluctantly contribute relevant data to, or even refuse to participate in FL. Therefore, in the application of FL, an important but also challenging issue is to motivate as many participants as possible to provide high-quality data to FL. In this paper, we propose an incentive mechanism for FL based on the continuous zero-determinant(CZD) strategies from the perspective of game theory. We first model the interaction between the server and the devices during the FL process as a continuous iterative game. We then apply the CZD strategies for two players and then multiple players to optimize the social welfare of FL, for which we prove that the server can keep social welfare at a high and stable level. Subsequently, we design an incentive mechanism based on the CZD strategies to attract devices to contribute all of their high-accuracy data to FL.Finally, we perform simulations to demonstrate that our proposed CZD-based incentive mechanism can indeed generate high and stable social welfare in FL.

Zero-determinant strategies in iterated multi-strategy games

Self-serving,rational agents sometimes cooperate to their mutual benefit.The two-player iterated prisoner′s dilemma game is a model for including the emergence of cooperation.It is generally believed that there is no simple ultimatum strategy which a player can control the return of the other participants.The zero-determinant strategy in the iterated prisoner′s dilemma dramatically expands our understanding of the classic game by uncovering strategies that provide a unilateral advantage to sentient players pitted against unwitting opponents.However,strategies in the prisoner′s dilemma game are only two strategies.Are there these results for general multi-strategy games?To address this question,the paper develops a theory for zero-determinant strategies for multi-strategy games,with any number of strategies.The analytical results exhibit a similar yet different scenario to the case of two-strategy games.The results are also applied to the Snowdrift game,the Hawk-Dove game and the Chicken game.

Zero-determinant strategy:An underway revolution in game theory

Repeated games describe situations where players interact with each other in a dynamic pattern and make decisions ac- cording to outcomes of previous stage games. Very recently, Press and Dyson have revealed a new class of zero-determinant （ZD） strategies for the repeated games, which can enforce a fixed linear relationship between expected payoffs of two play- ers, indicating that a smart player can control her unwitting co-player＇s payoff in a unilateral way [Proc. Acad. Natl. Sci. USA 109, 10409 （2012）]. The theory of ZD strategies provides a novel viewpoint to depict interactions among players, and fundamentally changes the research paradigm of game theory. In this brief survey, we first introduce the mathematical framework of ZD strategies, and review the properties and constrains of two specifications of ZD strategies, called pinning strategies and extortion strategies. Then we review some representative research progresses, including robustness analysis, cooperative ZD strategy analysis, and evolutionary stability analysis. Finally, we discuss some significant extensions to ZD strategies, including the multi-player ZD strategies, and ZD strategies under noise. Challenges in related research fields are also listed.

Equalizer Zero-Determinant Strategy in Discounted Repeated Stackelberg Asymmetric Game

This paper focuses on the performance of equalizer zero-determinant(ZD)strategies in discounted repeated Stackelberg asymmetric games.In the leader-follower adversarial scenario,the strong Stackelberg equilibrium(SSE)deriving from the opponents’best response(BR),is technically the optimal strategy for the leader.However,computing an SSE strategy may be difficult since it needs to solve a mixed-integer program and has exponential complexity in the number of states.To this end,the authors propose an equalizer ZD strategy,which can unilaterally restrict the opponent’s expected utility.The authors first study the existence of an equalizer ZD strategy with one-to-one situations,and analyze an upper bound of its performance with the baseline SSE strategy.Then the authors turn to multi-player models,where there exists one player adopting an equalizer ZD strategy.The authors give bounds of the weighted sum of opponents’s utilities,and compare it with the SSE strategy.Finally,the authors give simulations on unmanned aerial vehicles(UAVs)and the moving target defense(MTD)to verify the effectiveness of the proposed approach.

A potential game-based outsourcing computation framework for multiple calculators

Outsourcing computation enables a computationally weak client to outsource the computation of a function f to a more powerful but untrusted server.The traditional outsourcing computation model forbids communication between players,but it has little effect.Based on the game theory,this paper establishes an outsourcing computation model which is more in line with the actual scene.Firstly,we construct a structural mapping relationship between security outsourcing computation and the optimization problem.Secondly,by designing the individual potential function and the global potential function,the individual goal is consistent with the global goal to ensure the correctness of the calculation results.Finally,in the information exchange environment between calculators,we construct a Zero-determinant strategy to ensure that the calculator chooses the strategy according to the predetermined target.