Automated Bilateral Bargaining about Multiple Attributes in a One­ to ­Many Setting

Negotiations are an important way of reaching agreements between selfish autonomous agents. In this paper we focus on one-to-many bargaining within the context of agent-mediated electronic commerce. We consider an approach where a seller agent negotiates over multiple interdependent attributes with many buyer agents in a bilateral fashion. In this setting, "fairness", which corresponds to the notion of envy-freeness in auctions, may be an important business constraint. For the case of virtually unlimited supply (such as information goods), we present a number of one-to-many bargaining strategies for the seller agent, which take into account the fairness constraint, and consider multiple attributes simultaneously. We compare the performance of the bargaining strategies using an evolutionary simulation, especially for the case of impatient buyers. Several of the developed strategies are able to extract almost all the surplus; they utilize the fact that the setting is one-to-many, even though bargaining is bilateral

Autonomous agents in bargaining games : an evolutionary investigation of fundamentals, strategies, and business applications

Bargaining is becoming increasingly important due to developments within the field of electronic commerce, especially the development of autonomous software agents. Software agents are programs which, given instructions from a user, are capable of autonomously and intelligently realise a given task. By means of such agents, the bargaining process can be automated, allowing products and services together with related conditions, such as warranty and delivery time, to be flexible and tuned to the individual preferences of the people concerned. In this theses we concentrate on both fundamental aspects of bargaining as well as business-related applications of automated bargaining using software agents. The fundamental part investigates bargaining outcomes within a stylised world, and the factors that influence these outcomes. This can provide insights for the production of software agents, strategies, and setting up bargaining rules for practical situations. We study these aspects using computational simulations of bargaining agents. Hereby we consider adaptive systems, i.e., where agents learn to adjust their bargaining strategy given past experience. This learning behaviour is simulated using evolutionary algorithms. These algorithms originate from the field of artificial intelligence, and are inspired by the biological theory of evolution. Originally, evolutionary algorithms were designed for solving optimisation problems, but they are now increasingly being used within economics for modelling human learning behaviour. Besides computational simulations, we also consider mathematical solutions from game theory for relatively simple cases. Game theory is mainly concerned with the “rational man”, that is, with optimal outcomes within an stylised setting (or game) where people act rationally. We use the game-theoretic outcomes to validate the computational experiments. The advantage of computer simulations is that less strict assumptions are necessary, and that more complex interactions that are closer to real-world settings can be investigated. First of all, we study a bargaining setting where two players exchange offers and counter offers, the so-called alternating-offers game. This game is frequently used for modelling bargaining about for instance the price of a product or service. It is also important, however, to allow other product- and service-related aspects to be negotiated, such as quality, delivery time, and warranty. This enables compromises by conceding on less important issues and demanding a higher value for relatively important aspects. This way, bargaining is less competitive and the resulting outcome can be mutually beneficial. Therefore, we investigate using computational simulations an extended version of the alternating-offers game, where multiple aspects are negotiated concurrently. Moreover, we apply game theory to validate the results of the computational experiments. The simulation shows that learning agents are capable of quickly finding optimal compromises, also called Pareto-efficient outcomes. In addition, we study the effects of time pressure that arise if negotiations are broken off with a small probability, for example due to external eventualities. In absence of time pressure and a maximum number of negotiation rounds, outcomes are very unbalanced: the player that has the opportunity to make a final offer proposes a take-it-or-leave-it offer in the last round, which leaves the other player with a deal that is only slightly better than no deal at all. With relatively high time pressure, on the other hand, the first offer is most important and almost all agreements are reached in the first round. Another interesting result is that the simulation outcomes after a long period of learning in general coincide with the results from game theory, in spite of the fact that the learning agents are not “rational”. In reality, not only the final outcome is important, but also other factors play a role, such as the fairness of an offer. Using the simulation we study the influence of such fairness norms on the bargaining outcomes. The fairness norms result in much more balanced outcomes, even with no time pressure, and seem to be closer outcomes in the real world. Negotiations are rarely isolated, but can also be influenced by external factors such as additional bargaining opportunities. We therefore also consider bargaining within a market-like setting, where both buyers and sellers can bargain with several opponents before reaching an agreement. The negotiations are executed consecutively until an agreement is reached or no more opportunities are available. Each bargaining game is reduced to a single round, where player 1 makes an offer and player 2 can only respond by rejecting or accepting this offer. Using an evolutionary simulation we study several properties of this market game. It appears that the outcomes depend on the information that is available to the players. If players are informed about the bargaining opportunities of their opponents, the first player in turn has the advantage and always proposes a take-it-or-leave-it deal that leaves the other player with a relatively poor outcome. This outcome is consistent with a game-theoretic analysis which we also present in this thesis. If this information is not available, a theoretical analysis is very hard. The evolutionary simulation, however, shows that in this case the responder obtains a better deal. This occurs because the first player can no longer anticipate the response of the other player, and therefore bids lower to avoid a disagreement. In this thesis, we additionally consider other factors that influence the outcomes of the market game, such as negotiation over multiple issues simultaneously, search costs, and break off probabilities. Besides fundamental issues, this thesis presents a number of business-related applications of automated bargaining, as well as generic bargaining strategies for agents that can be employed in related areas. As a first application, we introduce a framework where negotiation is used for recommending shops to customers, for example on a web page of an electronic shopping mall. Through a market-driven auction a relevant selection of shops is determined in a distributed fashion. This is achieved by selling a limited number of banner spaces in an electronic auction. For each arriving customer on the web page, shops can automatically place bids for this “customer attention space” through their shop agents. These software agents bid based on a customer profile, containing personal data of the customer, such as age, interests, and/or keywords in a search query. The shop agents are adaptive and learn, given feedback from the customers, which profiles to target and how much to bid in the auction. The highest bidders are then selected and displayed to the customer. The feasibility of this distributed approach for matching shops to customers is demonstrated using an evolutionary simulation. Several customer models and auction mechanisms are studied, and we show that the market-based approach results in a proper selection of shops for the customers. Bargaining can be especially beneficial if not only the price, but other aspects are considered as well. This allows for example to customise products and services to the personal preferences of a user. We developed a system makes use of these properties for selling and personalising so-called information goods, such as news articles, software, and music. Using the alternating-offers protocol, a seller agent negotiates with several buyers simultaneously about a fixed price, a per-item price, and the quality of a bundle of information goods. The system is capable of taking into account important business-related conditions such as the fairness of the negotiation. The agents combine a search strategy and a concession strategy to generate offers in the negotiations. The concession strategy determines the amount the agent will concede each round, whereas the search strategy takes care of the personalisation of the offer. We introduce two search strategies in this thesis, and show through computer experiments that the use of these strategies by a buyer and seller agent, result in personalised outcomes, also when combined with various concession strategies. The search strategies presented here can be easily applied to other domains where personalisation is important. In addition, we also developed concession strategies for the seller agent that can be used in settings where a single seller agent bargains with several buyer agents simultaneously. Even if bargaining itself is bilateral (i.e., between two parties), a seller agent can actually benefit from the fact that several such negotiations occur concurrently. The developed strategies are focussed on domains where supply is flexible and can be adjusted to meet demand, like for information goods. We study fixed strategies, time-dependent strategies and introduce several auction-inspired strategies. Auctions are often used when one party negotiates with several opponents simultaneously. Although the latter strategies benefit from the advantages of auctions, the actual negotiation remains bilateral and consists of exchanging offers and counter offers. We developed an evolutionary simulation environment to evaluate the seller agent’s strategies. We especially consider the case where buyers are time-impatient and under pressure to reach agreements early. The simulations show that the auction-inspired strategies are able to obtain almost maximum profits from the negotiations, given sufficient time pressure of the buyers

Optimal bidding strategies for simultaneous Vickrey auctions with perfect substitutes

In this paper, we derive optimal bidding strategies for a global bidder who participates in multiple, simultaneous second-price auctions with perfect substitutes. We first consider a model where all other bidders are local and participate in a single auction. For this case, we prove that, assuming free disposal, the global bidder should always place non-zero bids in all available auctions, irrespective of the local bidders’ valuation distribution. Furthermore, for nondecreasing valuation distributions, we prove that the problem of finding the optimal bids reduces to two dimensions. These results hold both in the case where the number of local bidders is known and when this number is determined by a Poisson distribution. In addition, by combining analytical and simulation results, we demonstrate that similar results hold in the case of several global bidders, provided that the market consists of both global and local bidders. Finally, we address the efficiency of the overall market, and show that information about the number of local bidders is an important determinant for the way in which a global bidder affects efficiency

Bargaining with posterior opportunities: an evolutionary social simulation

Negotiations have been extensively studied theoretically throughout the years. A well-known bilateral approach is the ultimatum game, where two agents negotiate on how to split a pie or a `dollar': the proposer makes an offer and responder can choose to accept or reject. In this paper a natural extension of the ultimatum game is presented, in which both agents can negotiate with other opponents in case of a disagreement. This way the basics of a competitive market are modelled where for instance a buyer can try several sellers before making a purchase decision. The game is investigated using an evolutionary simulation. The outcomes appear to depend largely on the information available to the agents. We find that if the agents' number of future bargaining opportunities is commonly known, the proposer has the advantage. If this information is held private, however, the responder can obtain a larger share of the pie. For the first case we also provide a game-theoretic analysis and compare the outcome with evolutionary results. Furthermore, the effects of search costs and allowing multiple issues to be negotiated simultaneously are investigated

Equilibrium selection in alternating-offers bargaining models : the evolutionary computing approach

This paper studies the dynamic and equilibrium-selecting behavior of a multi-agent system consisting of adaptive bargaining agents. We model an adaptive agent as a collection of strategies which is optimized by an evolutionary algorithm (EA). EAs are stochastic search methods based upon the principles of natural genetic systems. These algorithms have been used in the past, with considerable success, to solve difficult optimization problems. Examples include problems with huge search spaces, multiple local optima, discontinuities, and noise. Adaptive agents learn in three different ways in an evolutionary setting: (i) by selection and reproduction of successful strategies, (ii) by recombining or ``crossing over'' previously-tested strategies, and (iii) by random experimentation (by ``mutating'' existing strategies). Such agents are boundedly rational because they only experience the profit of their interactions with other agents and learn by trial-and-error instead of abstract reasoning. Their equilibrium-selecting behavior is interpreted in this paper by comparison with game-theoretic (subgame-perfect equilibrium) predictions for fully rational agents. This paper shows that game-theoretic approaches are very useful to interpret equilibrium-selecting behavior in evolutionary systems of adaptive bargaining agents. The adaptive agents are boundedly rational because they only experience the profit of their interactions with other agents. Nevertheless, they display behavior that is surprisingly "rational" and fully informed in many instances. Agreement between theory and experiment is especially good when the agents experience an intermediate time pressure. In extreme situations (i.e., when time pressure becomes either strong or weak) significant deviations from game-theoretic predictions can occur, however. A good example is the case of extreme time pressure. In this case, highly nonlinear transients can occur if the deal reached by the adaptive agents approaches the extreme outcome predicted by game theory. Two other experimental observations should also be mentioned here. First, the finite horizon of the negotiations is not always fully exploited by the last agent in turn (even if time pressure is rather weak). In fact, the boundedly-rational agents often act as if the length of the game is actually much longer. This lends more support to the "infinite-horizon" assumption frequently employed in game-theoretic work. This approximation may yield surprisingly accurate results when the agents do not perceive the deadline of the negotiations. Second, we observe (and explain) discrepancies between theory and experiment if the agents experience an unequal time pressure. More in general, this work presents a systematic validation of evolutionary and computational techniques in the field of bargaining. Our model has also served as a starting point for further explorations. Several important topics have been addressed in these works: complex multi-issue and multi-opponent bargaining problems, economic modelling issues, learning by co-evolution, the development of powerful bargaining strategies, etc. We hope that these different lines of research will be extended further in future works

Competing sellers in online markets: reserve prices, shill bidding and auction fees

In this paper, we consider competition between sellers offering similar items in concurrent online auctions, where each seller must set its individual auction parameters (such as the reserve price) in such a way as to attract buyers. We show that there exists a pure Nash equilibrium in the case of two sellers with asymmetric production costs. In addition, we show that, rather than setting a reserve price, a seller can further improve its utility by shill bidding (i.e., pretending to be a buyer in order to bid in its own auction). But, using an evolutionary simulation, we show that this shill bidding introduces inefficiencies within the market. However, we then go on to show that these inefficiencies can be reduced when the mediating auction institution uses appropriate auction fees that deter sellers from submitting shill bids

Equilibrium selection in alternating-offers bargaining models: the evolutionary computing approach

A systematic validation of evolutionary techniques in the field of bargaining is presented. For this purpose, the dynamic and equilibrium-selecting behavior of a multi-agent system consisting of adaptive bargaining agents is investigated. The agents' bargaining strategies are updated by an evolutionary algorithm (EA), an innovative computational method to simulate collective learnin g in societies of boundedly-rational agents. Negotiations between the agents are governed by the well-known``alternating-offers' protocol. Using this protocol, the influence of various important factors (like the finite length of the game, time preferences, exogenous breakdown, and risk aversiveness) is investigated. We show that game theory can be used successfully to interpret the equilibrium-selecting behavior observed in computational experiments with adaptive bargaining agents. Agreement between theory and experiment is especially good when the agents experience an intermediate time pressure. Deviations from classical game theory are, however, observed in several experiments. Violent nonlinear oscillations may for instance occur in the single-stage ultimatum game. We demonstrate that the specific evolutionary model governing agent selection is an important factor under these conditions. In multiple-stage games, the evolving agents do not always fully perceive and exploit the finite horizon of the game (even when time pressure is weak). This effect can be attributed to the boundedly-rational behavior of the adapting agents. Furthermore, when the agents discount their payoffs at a different rate, the agent with the largest discount factor is not able to exploit his bargaining power completely, being under pressure by his impatient opponent to reach an early agreement. Negotiations over multiple issues, a particularly important aspect of electronic trading, are studied in a companion paper cite{Gerding:00. We are currently investigating the behavior of more complex and powerful bargaining agents

Competitive market-based allocation of consumer attention space

The amount of attention space available for recommending suppliers to consumers on e-commerce sites is typically limited. We present a competitive distributed recommendation mechanism based on adaptive software agents for efficiently allocating the 'consumer attention space', or banners. In the example of an electronic shopping mall, the task is delegated to the individual shops, each of which evaluates the information that is available about the consumer and his or her interests (e.g. keywords, product queries, and available parts of a profile). Shops make a monetary bid in an auction where a limited amount of 'consumer attention space' for the arriving consumer is sold. Each shop is represented by a software agent that bids for each consumer. This allows shops to rapidly adapt their bidding strategy to focus on consumers interested in their offerings. For various basic and simple models for on-line consumers, shops, and profiles, we demonstrate the feasibility of our system by evolutionary simulations as in the field of agent-based computational economics (ACE). We also develop adaptive software agents that learn bidding-strategies, based on neural networks and strategy exploration heuristics. Furthermore, we address the commercial and technological advantages of this distributed market-based approach. The mechanism we describe is not limited to the example of the electronic shopping mall, but can easily be extended to other domains

Multi-attribute bilateral bargaining in a one-to-many setting

Negotiations are an important way of reaching agreements between selfish autonomous agents. In this paper we focus on one-to-many bargaining within the context of agent-mediated electronic commerce. We consider an approach where a seller negotiates over multiple interdependent attributes with many buyers individually. Bargaining is conducted in a bilateral fashion, using an alternating-offers protocol. In such a one-to-many setting, “fairness,” which corresponds to the notion of envy-freeness in auctions, may be an important business constraint. For the case of virtually unlimited supply (such as information goods), we present a number of one-to-many bargaining strategies for the seller, which take into account the fairness constraint, and consider multiple attributes simultaneously. We compare the performance of the bargaining strategies using an evolutionary simulation, especially for the case of impatient buyers and small premature bargaining break off probability. Several of the developed strategies are able to extract almost all the surplus; they utilize the fact that the setting is one-to-many, even though bargaining occurs in a bilateral fashion