Autonomous Agents in Bargaining Games: An Evolutionary Investigation of Fundamentals, Strategies, and Business Applications

Abstract

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.

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ORCID for E.H. Gerding: orcid.org/0000-0001-7200-552X

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