Moshe Tennenholtz

On social laws for artificial agent societies: off-line design

Abstract We are concerned with the utility of social laws in a computational environment, laws which guarantee the successful coexistence of multiple programs and programmers. In this paper we are interested in the off-line design of social laws, where we as designers must decide ahead of time on useful social laws. In the first part of this paper we suggest the use of social laws in the domain of mobile robots, and prove analytic results about the usefulness of this approach in that setting. In the second part of this paper we present a general model of social law in a computational system, and investigate some of its properties. This includes a definition of the basic computational problem involved with the design of multi-agent systems, and an investigation of the automatic synthesis of useful social laws in the framework of a model which refers explicitly to social laws.

On the emergence of social conventions: modeling, analysis, and simulations

Abstract We define the notion of social conventions in a standard game-theoretic framework, and identify various criteria of consistency of such conventions with the principle of individual rationality. We then investigate the emergence of such conventions in a stochastic setting; we do so within a stylized framework currently popular in economic circles, namely that of stochastic games . This framework comes in several forms; in our setting agents interact with each other through a random process, and accumulate information about the system. As they do so, they continually reevaluate their current choice of strategy in light of the accumulated information. We introduce a simple and natural strategy-selection rule, called highest cumulative reward (HCR). We show a class of games in which HCR guarantees eventual convergence to a rationally acceptable social convention. Most importantly, we investigate the efficiency with which such social conventions are achieved. We give an analytic lower bound on this rate, and then present results about how HCR works out in practice. Specifically, we pick one of the most basic games, namely a basic coordination game (as defined by Lewis), and through extensive computer simulations determine not only the effect of applying HCR, but also the subtle effects of various system parameters, such as the amount of memory and the frequency of update performed by all agents.

Trust-based recommendation systems: an axiomatic approach

High-quality, personalized recommendations are a key feature in many online systems. Since these systems often have explicit knowledge of social network structures, the recommendations may incorporate this information. This paper focuses on networks that represent trust and recommendation systems that incorporate these trust relationships. The goal of a trust-based recommendation system is to generate personalized recommendations by aggregating the opinions of other users in the trust network. In analogy to prior work on voting and ranking systems, we use the axiomatic approach from the theory of social choice. We develop a set of five natural axioms that a trust-based recommendation system might be expected to satisfy. Then, we show that no system can simultaneously satisfy all the axioms. However, for any subset of four of the five axioms we exhibit a recommendation system that satisfies those axioms. Next we consider various ways of weakening the axioms, one of which leads to a unique recommendation system based on random walks. We consider other recommendation systems, including systems based on personalized PageRank, majority of majorities, and minimum cuts, and search for alternative axiomatizations that uniquely characterize these systems. Finally, we determine which of these systems are incentive compatible, meaning that groups of agents interested in manipulating recommendations can not induce others to share their opinion by lying about their votes or modifying their trust links. This is an important property for systems deployed in a monetized environment.

Approximate mechanism design without money

The literature on algorithmic mechanism design is mostly concerned with game-theoretic versions of optimization problems to which standard economic money-based mechanisms cannot be applied efficiently. Recent years have seen the design of various truthful approximation mechanisms that rely on enforcing payments. In this paper, we advocate the reconsideration of highly structured optimization problems in the context of mechanism design. We argue that, in such domains, approximation can be leveraged to obtain truthfulness without resorting to payments. This stands in contrast to previous work where payments are ubiquitous, and (more often than not) approximation is a necessary evil that is required to circumvent computational complexity. We present a case study in approximate mechanism design without money. In our basic setting agents are located on the real line and the mechanism must select the location of a public facility; the cost of an agent is its distance to the facility. We establish tight upper and lower bounds for the approximation ratio given by strategyproof mechanisms without payments, with respect to both deterministic and randomized mechanisms, under two objective functions: the social cost, and the maximum cost. We then extend our results in two natural directions: a domain where two facilities must be located, and a domain where each agent controls multiple locations.

Adaptive load balancing: a study in multi-agent learning

We study the process of multi-agent reinforcement learning in the context of load balancing in a distributed system, without use of either central coordination or explicit communication. We first define a precise framework in which to study adaptive load balancing, important features of which are its stochastic nature and the purely local information available to individual agents. Given this framework, we show illuminating results on the interplay between basic adaptive behavior parameters and their effect on system efficiency. We then investigate the properties of adaptive load balancing in heterogeneous populations, and address the issue of exploration vs. exploitation in that context. Finally, we show that naive use of communication may not improve, and might even harm system efficiency.

Ranking systems: the PageRank axioms

This paper initiates research on the foundations of ranking systems, a fundamental ingredient of basic e-commerce and Internet Technologies. In order to understand the essence and the exact rationale of page ranking algorithms we suggest the axiomatic approach taken in the formal theory of social choice. In this paper we deal with PageRank, the most famous page ranking algorithm. We present a set of simple (graph-theoretic, ordinal) axioms that are satisfied by PageRank, and moreover any page ranking algorithm that does satisfy them must coincide with PageRank. This is the first representation theorem of that kind, bridging the gap between page ranking algorithms and the mathematical theory of social choice.

Bundling equilibrium in combinatorial auctions

This paper analyzes ex post equilibria in the VCG combinatorial auctions. If Σ is a family of bundles of goods, the organizer may restrict the bundles on which the participants submit bids, and the bundles allocated to them, to be in Σ .T heΣ -VCG combinatorial auctions obtained in this way are known to be truth-telling mechanisms. In contrast, this paper deals with non-restricted VCG auctions, in which the buyers choose strategies that involve bidding only on bundles in Σ , and these strategies form an equilibrium. We fully characterize those Σ that induce an equilibrium in every VCG auction, and we refer to the associated equilibrium as a bundling equilibrium. The main motivation for studying all these equilibria, and not just the domination equilibrium, is that they afford a reduction of the communication complexity. We analyze the tradeoff between communication complexity and economic efficiency of bundling equilibrium.

Approximately optimal mechanism design via differential privacy

We study the implementation challenge in an abstract interdependent values model and an arbitrary objective function. We design a generic mechanism that allows for approximate optimal implementation of insensitive objective functions in ex-post Nash equilibrium. If, furthermore, values are private then the same mechanism is strategy proof. We cast our results onto two specific models: pricing and facility location. The mechanism we design is optimal up to an additive factor of the order of magnitude of one over the square root of the number of agents and involves no utility transfers. Underlying our mechanism is a lottery between two auxiliary mechanisms --- with high probability we actuate a mechanism that reduces players influence on the choice of the social alternative, while choosing the optimal outcome with high probability. This is where differential privacy is employed. With the complementary probability we actuate a mechanism that may be typically far from optimal but is incentive compatible. The joint mechanism inherits the desired properties from both.

Modeling agents as qualitative decision makers

Abstract We investigate the semantic foundations of a method for modeling agents as entities with a mental state which was suggested by McCarthy and by Newell. Our goals are to formalize this modeling approach and its semantics, to understand the theoretical and practical issues that it raises, and to address some of them. In particular, this requires specifying the models parameters and how these parameters are to be assigned (i.e., their grounding ). We propose a basic model in which the agent is viewed as a qualitative decision maker with beliefs, preferences, and a decision strategy; and we show how these components would determine the agents behavior. We ground this model in the agents interaction with the world, namely, in its actions. This is done by viewing model construction as a constraint satisfaction problem in which we search for a model consistent with the agents behavior and with our general background knowledge. In addition, we investigate the conditions under which a mental state model exists, characterizing a class of “goal-seeking” agents that can be modeled in this manner; and we suggest two criteria for choosing between consistent models, showing conditions under which they lead to a unique choice of model.

Efficient learning equilibrium

We introduce efficient learning equilibrium (ELE), a normative approach to learning in noncooperative settings. In ELE, the learning algorithms themselves are required to be in equilibrium. In addition, the learning algorithms must arrive at a desired value after polynomial time, and a deviation from the prescribed ELE becomes irrational after polynomial time. We prove the existence of an ELE (where the desired value is the expected payoff in a Nash equilibrium) and of a Pareto-ELE (where the objective is the maximization of social surplus) in repeated games with perfect monitoring. We also show that an ELE does not always exist in the imperfect monitoring case. Finally, we discuss the extension of these results to general-sum stochastic games.