Incentive Stackelberg Mean-payoff Games

We introduce and study incentive equilibria for multi-player meanpayoff games. Incentive equilibria generalise well-studied solution concepts such as Nash equilibria and leader equilibria (also known as Stackelberg equilibria). Recall that a strategy profile is a Nash equilibrium if no player can improve his payoff by changing his strategy unilaterally. In the setting of incentive and leader equilibria, there is a distinguished player called the leader who can assign strategies to all other players, referred to as her followers. A strategy profile is a leader strategy profile if no player, except for the leader, can improve his payoff by changing his strategy unilaterally, and a leader equilibrium is a leader strategy profile with a maximal return for the leader. In the proposed case of incentive equilibria, the leader can additionally influence the behaviour of her followers by transferring parts of her payoff to her followers. The ability to incentivise her followers provides the leader with more freedom in selecting strategy profiles, and we show that this can indeed improve the payoff for the leader in such games. The key fundamental result of the paper is the existence of incentive equilibria in mean-payoff games. We further show that the decision problem related to constructing incentive equilibria is NP-complete. On a positive note, we show that, when the number of players is fixed, the complexity of the problem falls in the same class as two-player mean-payoff games. We also present an implementation of the proposed algorithms, and discuss experimental results that demonstrate the feasibility of the analysis of medium sized games.Comment: 15 pages, references, appendix, 5 figure

Fragility and Robustness in Mean-Payoff Adversarial Stackelberg Games

Two-player mean-payoff Stackelberg games are nonzero-sum infinite duration games played on a bi-weighted graph by Leader (Player 0) and Follower (Player 1). Such games are played sequentially: first, Leader announces her strategy, second, Follower chooses his best-response. If we cannot impose which best-response is chosen by Follower, we say that Follower, though strategic, is adversarial towards Leader. The maximal value that Leader can get in this nonzero-sum game is called the adversarial Stackelberg value (ASV) of the game. We study the robustness of strategies for Leader in these games against two types of deviations: (i) Modeling imprecision - the weights on the edges of the game arena may not be exactly correct, they may be delta-away from the right one. (ii) Sub-optimal response - Follower may play epsilon-optimal best-responses instead of perfect best-responses. First, we show that if the game is zero-sum then robustness is guaranteed while in the nonzero-sum case, optimal strategies for ASV are fragile. Second, we provide a solution concept to obtain strategies for Leader that are robust to both modeling imprecision, and as well as to the epsilon-optimal responses of Follower, and study several properties and algorithmic problems related to this solution concept

The Adversarial Stackelberg Value in Quantitative Games

In this paper, we study the notion of adversarial Stackelberg value for two-player non-zero sum games played on bi-weighted graphs with the mean-payoff and the discounted sum functions. The adversarial Stackelberg value of Player 0 is the largest value that Player 0 can obtain when announcing her strategy to Player 1 which in turn responds with any of his best response. For the mean-payoff function, we show that the adversarial Stackelberg value is not always achievable but ?-optimal strategies exist. We show how to compute this value and prove that the associated threshold problem is in NP. For the discounted sum payoff function, we draw a link with the target discounted sum problem which explains why the problem is difficult to solve for this payoff function. We also provide solutions to related gap problems

The Adversarial Stackelberg Value in Quantitative Games

In this paper, we study the notion of adversarial Stackelberg value for two-player non-zero sum games played on bi-weighted graphs with the mean-payoff and the discounted sum functions. The adversarial Stackelberg value of Player 0 is the largest value that Player 0 can obtain when announcing her strategy to Player 1 which in turn responds with any of his best response. For the mean-payoff function, we show that the adversarial Stackelberg value is not always achievable but epsilon-optimal strategies exist. We show how to compute this value and prove that the associated threshold problem is in NP. For the discounted sum payoff function, we draw a link with the target discounted sum problem which explains why the problem is difficult to solve for this payoff function. We also provide solutions to related gap problems.Comment: long version of an ICALP'20 pape

Fragility and Robustness in Mean-payoff Adversarial Stackelberg Games

Two-player mean-payoff Stackelberg games are nonzero-sum infinite duration games played on a bi-weighted graph by a leader (Player~0) and a follower (Player~1). Such games are played sequentially: first, the leader announces her strategy, second, the follower chooses his strategy. This pair of strategies defines a unique infinite path in the graph and both players receive their respective payoff computed as the mean of the rewards that they receive when traversing edges along the infinite path. As a consequence, if we assume that the follower is rational then we can deduce that the follower's response to the leader strategy is a strategy that maximizes his payoff against the strategy proposed by the leader; it is thus a best-response to this strategy. Knowing that, the leader should choose a strategy that maximizes the payoff that she receives when the follower chooses a best-response to her strategy. If we cannot impose which best-response is chosen by the follower, we say that the follower, though strategic, is \emph{adversarial} towards the leader. The maximal value that the leader can get in this nonzero-sum game is called the {\em adversarial Stackelberg value} of the game. First, we show that the nonzero-sum nature of the mean-payoff Stackelberg game makes it fragile against modelling imprecisions. This is in contrast with mean-payoff games in the zero-sum setting which are robust. Second, we show how robustness is recovered when considering $\epsilon$-best responses of the follower instead of best-responses only. This lead to the notion of $\epsilon$-adversarial Stackelberg value. Third, we provide algorithms to decide the threshold problem for this robust value as well as ways to compute it effectively. Finally, we characterize the memory needed by the strategies of the leader and the follower in these games.Comment: Added discussion on fragility and robustness of mean-payoff games for both non-zero sum and zero-sum cases, and new results on NP-completeness of games restricted to memoryless strategies of the leade

Software Engineering and Formal Methods [electronic resource] : 14th International Conference, SEFM 2016, Held as Part of STAF 2016, Vienna, Austria, July 4-8, 2016, Proceedings /

This book constitutes the proceedings of the 14th International Conference on Software Engineering and Formal Methods, SEFM 2016, held as part of STAF 2016, in Vienna, Austria, in July 2016. The 20 full and 5 short papers presented in this volume were carefully reviewed and selected from 88 submissions. They were organized in topical sections named: concurrency and non-interference; program analysis; model checking; verification; interaction and adaptation; and development methods.Invited Papers -- Abstractions, Semantic Models and Analysis Tools for Concurrent Systems: Progress and Open Problems -- Satisfiability Checking: Theory and Applications -- Concurrency and Non-Interference -- Automatic Derivation of Platform Noninterference Properties -- Linearizability and Causality -- Refinement-based verification of Communicating Unstructured Code -- Guided Dynamic Symbolic Execution Using Subgraph Control-Flow Information (short paper) -- Program Analysis -- Correlating Structured Inputs and Outputs in Functional Specifications -- Combining Predicate Abstraction with Fixpoint Approximations -- Finding Boundary Elements in Ordered Sets with Application to Safety and Requirements Analysis -- Combining Abstract Interpretation with Symbolic Execution for a Static Value Range Analysis of Block Diagrams -- Model Checking -- Program Generation using Simulated Annealing and Model Checking -- LTL Parameter Synthesis of Parametric Timed Automata -- Model checking simulation rules for linearizability -- LTL Model Checking under Fairness in ProB (short paper) -- Verification -- Counterexamples from Proof Failures in SPARK -- Proving Termination of Programs with Bitvector Arithmetic by Symbolic Execution -- SMT-based automatic proof of ASM model refinement -- Coq Implementation of OO Verification Framework VeriJ (short paper) -- Towards a Proof Framework for Information Systems with Weak Consistency (short paper) -- Interaction and Adaptation -- A Cognitive Framework based on Rewriting Logic for the Analysis of Interactive Systems -- Incentive Stackelberg Mean-payoff Games -- Stability-based Adaptation of Asynchronously Communicating Software -- Compliance Checking in the Open Payments Ecosystem (short paper) -- Development Methods -- CoCoSpec: A mode aware contract language -- Modularizing Crosscutting Concerns in Component-Based Systems -- Tightening a Contract Refinement -- BMotionWeb: A Tool for Rapid Creation of Formal Prototypes.This book constitutes the proceedings of the 14th International Conference on Software Engineering and Formal Methods, SEFM 2016, held as part of STAF 2016, in Vienna, Austria, in July 2016. The 20 full and 5 short papers presented in this volume were carefully reviewed and selected from 88 submissions. They were organized in topical sections named: concurrency and non-interference; program analysis; model checking; verification; interaction and adaptation; and development methods