Bidding Strategies in the Swedish Housing Market
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Bidding strategies in the Swedish housing market Malin Norling Sofia Hjulfors Autumn semester 2016 Bachelor thesis, 15 hp Bachelor degree of mathematics, 180 hp Department of mathematics and mathematical statistics Acknowledgements We both would like to thank the real estate agencies and the people who helped us and provided bidding lists that we could analyze; Fastighetsbyr˚an- M¨olnlycke, Fastighetsbyr˚an- Bromma, Fastighetsbyr˚an- Kungs¨angen, M¨aklarhuset- Askim. We would specially like to thank Thomas Hansson from M¨aklarhuset, Askim, who we got the opportunity to interview to get a bigger understanding of the housing market and the strategies involved. I would like to dedicate this thesis to my loving father who passed away 2014. He always encouraged me to push my self and to believe in my self. He was and still is my role model. I also would like to thank my mom Anett, my sister Emelie, and my boyfriend Fredrik, for their love and support to me. - Malin Norling I am thankful for the support I got during this thesis process from friends and family. I would specially like to thank my father, Stefan, for pushing us both during this period, to inspire us to think outside the box. I would like to thank Pinja, may she rest in peace, that took us on inspiring walks when we needed breaks. - Sofia Hjulfors Abstract This report focuses on an introduction of game theoretical models and how they can be applied in the Swedish housing market. Game theory is a study of mathematical models of human conflicts and co- operation between rational decision makers within a competitive sit- uation. There are several different strategies that a player can use. In this thesis each strategy is assigned to one player. So how will the players behave in a game, and what strategy is the most successful? By using the software MatLab, the authors creates a game where the strategies assigned to each player gets randomly distributed budgets and are randomly selected to place bids during the game. The game is then played 1 000 000 times to see what strategy is the most success- ful. It is also tested to see what strategy is the most successful if the players have the same budgets. The authors conclude that in practice it is the size of the budget that determines who will win the bidding, hence there are minor differences between the different strategies in how much they pay on average to win. Sammanfattning Denna rapport fokuserar p˚aen introduktion av spelteoretiska mo- deller och hur de kan som kopplas till den svenska bostadsmarknaden. Spelteori ¨ar en studie om matematiska modeller f¨or m¨anskliga konflik- ter och samarbete mellan rationella beslutstagare i en konkurrensut- satt marknad. Det finns flera olika strategier en spelare kan anv¨anda sig av. I denna rapport blir varje spelare tilldelad en strategi. S˚afr˚agan st¨alls hur spelarna kommer att bete sig och vilken av strategierna som ¨ar den mest framg˚angsrika. Genom att anv¨anda programvaran MatLab, skapar f¨orfattarna ett program d¨ar varje strategi ¨ar tilldelad varje spelare och som helt slumpm¨assigt f˚aren budget och ¨aven blir slumpm¨assigt valda att spela, d.v.s l¨agga bud under spelets g˚ang.Spe- let spelas d¨arefter 1 000 000 g˚angerf¨or att se vilken av strategierna som ¨ar mest framg˚angsrik.Det ¨ar ¨aven testat att se vilken strategi som f˚arb¨ast resultat om de alla har samma budget. F¨orfattarna drar slutsatsen att i praktiken ¨ar det storleken p˚abudgeten som best¨ammer vem som vinner budgivningen, dock att det ¨aven finns mindre skillna- der mellan strategierna som best¨ammer hur mycket de i genomsnitt f˚arbetala n¨ar de vinner. "You need to learn the rules of the game, and then you have to play better than anyone else." - Albert Einstein Contents 1 Introduction 1 2 Game theory 3 2.1 Rules of the game . .3 2.1.1 Cooperative and non-cooperative games . .5 2.1.2 Simultaneous and sequential games . .6 2.2 Normal form games . .7 2.3 Nash equilibrium . .7 2.4 Extensive form games . .8 2.4.1 Extensive games with perfect information . .8 2.4.2 Extensive games with imperfect information . 10 2.5 Bayesian games . 10 2.6 Evolutionary game theory . 12 2.7 Auction theory . 13 3 The housing market 14 3.1 Interview with a real estate agent . 14 3.2 Auction rules . 15 3.3 Bidding strategies . 16 4 The auction game 18 4.1 Rules of the game . 18 4.2 The game . 19 5 Results and analysis of the game 20 6 Conclusion 24 A Appendix: MATLAB codes 28 A.1 The auction . 28 A.2 Bid counter . 31 A.3 Competitors left . 32 A.4 Winner . 32 A.5 Average . 32 A.6 Strategy 1 . 33 A.7 Strategy 2 . 34 A.8 Strategy 3 . 35 A.9 Strategy 4 . 37 A.10 Strategy 5 . 38 A.11 Strategy 6 . 39 List of Figures 1 The Sharing game . .9 2 Randomly distributed budgets . 20 3 Fixed budgets . 21 List of Tables 1 Average price paid from randomly played game . 21 2 Bidding list with random budgets . 23 Nomenclature 2 Element of [ Union \ Intersection ? Empty set × Cartesian product R Real numbers G Game i Player n Number of players N Set of all players, N = 1; :::; n Si Set of pure strategies for each player i 2 N,Si = s1; :::; sm ∗ ∗ ∗ ∗ Si Set of mixed strategies for each player i 2 N,Si = s1; :::; sn S Set of all strategic profiles, S = S1 × ::: × Sn Ai Set of possible actions for each player i 2 N,Ai = a1; :::; an I Set of information, I = I1; :::; In Θi Set of possible types for player i 2 N,Θi = θ1; :::; θn H Set of non-terminal nodes Z Set of terminal nodes, Z \ H = ? P Probability vector, P = (p1; :::; pm) U Payoff (utility) α Action function ρ Player function σ Successor function 1 Introduction Game theory is a mathematical tool that studies the analysis of solving strate- gic problems of interaction among decision-makers and was originally intro- duced by von Neumann and Morgenstern in 1944 [15]. Each game has a set of rules and involves one or more decision-makers (players), whose actions and moves affect both the player itself and the others [16]. The result of the game will therefore depend on the players' choices of strategic or random moves depending on information, preferences, possibilities, and reactions. There are a variety of solution concepts in game theory, for example the Nash equilibrium, who is arguably the most well-known to use to analyze possible outcomes. Game theory is broadly used in a numerous of fields in economics, in everyday life, politics, and other game-related situations [3]. The assumption of rational players is used in game theory [14]. Assuming each player is seeking maximum utility and that all other players are doing the same is essential for the logical predication of the game. Auctions are a particular type of game that are studied in a branch of game theory, which is known as auction theory. In many real-life situations we can find auctions and they are often found when dealing with economic trans- actions. Auction theory is therefore an important tool for understanding interaction among sellers and buyers. There are many different sets of rules for an auction that defines what type of auction it is. There is for example the sealed-bid auction of first and second price, the descending-price auc- tion, and the Japanese auction [17]. In this thesis, the authors will focus on the auction model for open ascending bids, which is the model used in the Swedish housing market. A potential value of applying auction theory to the housing market is to give real estate agents a better understanding of how the market work and also the possibilities to analyze consequences of possible rule changes. It is also important for the buyers in the housing market to understand how to get an object to a cheaper price by a well chosen strategy. There are, however, difficulties and challenges when applying auction theory in practical and real- life situations. There are unique circumstances for each auction, certain rules can lead to changes and some factors goes outside the usual auction theory. Such factors could involve bids that are placed before the start of the auction, the psychology and mind set of each bidder and need of reactive strategies etc. Despite this untapped potential, it thus remains unclear to what extent auc- tion theory applies. How should a game-theoretical model for the Swedish 1 housing market be constructed? The aim of this thesis is to give an introduction to game theory, with focus on the mathematical theory behind auctions, and also to research auctions in the Swedish housing market. The purpose is to see how the auctions are related to games and to study effectiveness of selected strategies used in the housing market. The problem formulation for this thesis has been to see if there is a game theoretical model for how rational players are behaving in a bidding game, which are represented by the rules that is in the Swedish housing market. The methodology was to see how game theory is a study of mathematical models of human conflict and cooperation between rational decision makers within a competitive situation. When implementing it into the Swedish hous- ing market and the bidding game, the authors used the game theory methods; extensive form, perfect and incomplete information, mixed and pure strate- gies, non-cooperative, and n-player.