DOCSLIB.ORG

UC Merced Proceedings of the Annual Meeting of the Cognitive Science Society

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
UC Merced Proceedings of the Annual Meeting of the Cognitive Science Society UC Merced Proceedings of the Annual Meeting of the Cognitive Science Society Title Language as a Tool for Thought: The Vocabulary of Games Facilitates Strategic Decision Making Permalink https://escholarship.org/uc/item/2n8028tv Journal Proceedings of the Annual Meeting of the Cognitive Science Society, 28(28) ISSN 1069-7977 Authors Keller, Josh Loewenstein, Jeffrey Publication Date 2006 Peer reviewed eScholarship.org Powered by the California Digital Library University of California Language as a Tool for Thought: The Vocabulary of Games Facilitates Strategic Decision Making Jeffrey Loewenstein ([email protected]) McCombs School of Business, 1 University Station B6300 Austin, TX 78712 USA Josh Keller ([email protected]) McCombs School of Business, 1 University Station B6300 Austin, TX 78712 USA Abstract thereby influence key decision makers to favor their desired policies. More than 60 years ago, the sociologist Mills People in competitive decision-making situations often make (1939) argued that problems are perceived relative to a poor choices because they inadequately understand the vocabulary. For example, what counts as murder seems decision they are to make, particularly because they fail to straightforward, but should differ substantially across consider contingencies such as how their opponent will react vegans, anti-abortion activists, lawyers, soldiers and the to their choice (Tor & Bazerman, 2004). Accordingly it would be useful to have a generally applicable vocabulary to guide (hopefully extinct) ritual practitioner of human sacrifice people towards effective interpretations of decision situations. (Clark, 1998). The vocabulary of games provides one such toolkit. We One role of language is to invoke particular framings or presented 508 participants with words from the vocabulary of interpretations. There are many decision-making studies that games, or some lesser form of support, on a tic-tac-toe could be viewed as such, particularly among studies of decision scenario. Participants then generated a course of framing effects (e.g., Larrick & Blount, 1997), although few action for a second competitive decision-making scenario. attribute their effects to language per se. For example, Participants presented with words from the vocabulary of Liberman, Samuels and Ross (2004) found that people games were more likely to transfer and generate sound explanations of contingencies than participants receiving the choosing in a prisoner’s dilemma situation were more likely same key information in other terms or lesser support. to cooperate if the situation was labeled a “Community Vocabularies not only invoke particular framings of decision game” than if it was labeled a “Wall Street game.” These situations, but can guide reasoning through those and labels invoked cultural norms, and hence people’s subsequent decisions as well. understanding of the decision to be made. As studies of priming and memory accessibility amply demonstrate, that Introduction which can reliably invoke is important. There are two basic steps to making a decision: Language not only invokes but also guides reasoning. understanding what is to be decided, then making the actual One way language does so is by providing and organizing decision (Brandenberger & Nalebuff, 1996; Newell & “tools for thinking” (Vygotsky, 1934; see also the related Simon, 1972). Most decision research makes assumptions proposal of culture as a toolkit, as in Swidler, 1986). The about how people understand the decision situation, and tool analogy runs as follows: just as work is easier if one has then analyzes how they subsequently make the decision. the right tool for the job, so too is it easier to reason through Considerably less decision research has examined the a decision if one uses appropriate words for describing it. systematic influences that lead people to their initial Also, if a hammer is available, one is more likely to think of understandings of decision-making situations (see, e.g., nailing something together—and analogously, knowledge of Bazerman, Curhan & Moore, 2000, for an argument on the a particular vocabulary makes it more likely one will use need for more such research). We agree with March (1994: that vocabulary to understand and make decisions about 211-212), who claimed that “understanding decision making situations. By this view of language, vocabularies do not involved understanding the ways in which language carries, determine whether someone can or cannot think of elaborates, and creates meaning.” The broad proposal something, but rather vocabularies make particular ideas guiding our research is that the vocabulary people use to and subsequent reasoning easier and more likely to occur. articulate a decision frames and guides their reasoning of Further, just as an individual tool is less useful than a that decision. toolbox of related tools for coordinated activity, so too are The words used to describe a decision should influence sets of words—vocabularies—more useful than individual how people understand the decision and accordingly what words (Loewenstein & Ocasio, 2005; Loewenstein & choices and actions seem most reasonable to make. Gentner, 2005). Political actors appear to assume this to be true, as indicated One final important aspect of conceptualizing by the resources they expend to “frame the debate” and vocabularies as toolkits is that just as the same tools can be 501 useful in a wide variety of settings and for a wide variety of four numbers guide their choices (Hristova & Grinberg, projects, vocabularies can also capture abstract ideas of 2005). People are even poor at recognizing a useful framing wide applicability. This is often the case for professional of a decision when directly presented a choice between two and expert vocabularies (jargon). For example, whether and (Blount & Larrick, 2000). The poor interpretation of initial how much to donate to public radio and how much effort to situations is a general concern that skews decision making put into writing one’s section of a co-authored first draft are and problem solving (Newell & Simon, 1972; Kershaw & quite different decisions, but both can be construed more Ohlsson, 2004). generally as decisions about cooperating in social If people perform poorly on a wide variety of decision dilemmas. Vocabularies are particularly useful for helping problems due to poor initial interpretations, then it would be people transfer abstract ideas and frameworks typically used useful to have a generally applicable vocabulary to guide in one context for use in understanding and making people towards effective interpretations of decision decisions in a novel situation (Gentner & Loewenstein, situations. Such a vocabulary would demarcate categories 2002; Loewenstein & Gentner, 2005). and suggest lines of reasoning that facilitate making sound choices across situations. The vocabulary of games provides The Vocabulary of Games one such toolkit. One important toolbox for thinking about decision making is the vocabulary of games (von Neumann & Morgenstern, Experiment 1 1944; Luce & Raiffa, 1957). Clearly there is more to game Experiment 1 examines whether receiving a simple subset theory than its vocabulary, but it is just as clear that learning of terms of the vocabulary of games could facilitate decision the vocabulary is part and parcel of learning the larger making requiring participants to consider contingencies. approach to understanding strategic decision making. First we presented people with a tic-tac-toe decision Minimax, the logic of backward induction and decision trees scenario, followed by a challenging decision scenario that, have become standard approaches to strategic decision like the Monty Hall and Acquiring a Company problems, making. Research in decision making highlights why these requires people to think through contingencies of what developments and subsequent training are so important: actions are possible for themselves and their counterparts. people often fail to think about what actions they and their This was a novel decision scenario about two people playing opponents can take in a competitive decision making an unusual party game (the scenario is presented in full in situation. the Appendix). The vocabulary terms were presented The best known problems used to highlight poor accompanying a tic-tac-toe decision scenario, allowing the interpretations and reasoning through contingencies are the actual text of the key decision scenario to remain constant, Acquiring a Company problem used by Max Bazerman and and to require participants to transfer it to a new situation. colleagues (e.g., Ball, Bazerman & Carroll, 1991; see also Thus there were three conditions: the vocabulary condition, Foreman & Murnighan, 1996) and the Monty Hall problem the “game-only” control condition (who were given the tic- (from the game show, “Let’s Make a Deal”, e.g., Burns & tac-toe decision scenario without the accompanying Wieth, 2004; Idson et al, 2004). In key ways, these vocabulary terms), and the “reversed” control condition problems are like the simple children’s game, tic-tac-toe, in (who completed the key decision scenario before the tic-tac- which two players attempt to get three marks in a row on a toe decision scenario in case that scenario in itself was 3x3 grid. In all of them, it is a poor strategy to decide what helpful). to do without first considering what the other person will do in response to that choice. To adults—perhaps because most Methods
Load more

Recommended publications
  • 1 Sequential Games
    1 Sequential Games We call games where players take turns moving “sequential games”. Sequential games consist of the same elements as normal form games –there are players, rules, outcomes, and payo¤s. However, sequential games have the added element that history of play is now important as players can make decisions conditional on what other players have done. Thus, if two people are playing a game of Chess the second mover is able to observe the …rst mover’s initial move prior to making his initial move. While it is possible to represent sequential games using the strategic (or matrix) form representation of the game it is more instructive at …rst to represent sequential games using a game tree. In addition to the players, actions, outcomes, and payo¤s, the game tree will provide a history of play or a path of play. A very basic example of a sequential game is the Entrant-Incumbent game. The game is described as follows: Consider a game where there is an entrant and an incumbent. The entrant moves …rst and the incumbent observes the entrant’sdecision. The entrant can choose to either enter the market or remain out of the market. If the entrant remains out of the market then the game ends and the entrant receives a payo¤ of 0 while the incumbent receives a payo¤ of 2. If the entrant chooses to enter the market then the incumbent gets to make a choice. The incumbent chooses between …ghting entry or accommodating entry. If the incumbent …ghts the entrant receives a payo¤ of 3 while the incumbent receives a payo¤ of 1.
    [Show full text]
  • Lecture Notes
    GRADUATE GAME THEORY LECTURE NOTES BY OMER TAMUZ California Institute of Technology 2018 Acknowledgments These lecture notes are partially adapted from Osborne and Rubinstein [29], Maschler, Solan and Zamir [23], lecture notes by Federico Echenique, and slides by Daron Acemoglu and Asu Ozdaglar. I am indebted to Seo Young (Silvia) Kim and Zhuofang Li for their help in finding and correcting many errors. Any comments or suggestions are welcome. 2 Contents 1 Extensive form games with perfect information 7 1.1 Tic-Tac-Toe ........................................ 7 1.2 The Sweet Fifteen Game ................................ 7 1.3 Chess ............................................ 7 1.4 Definition of extensive form games with perfect information ........... 10 1.5 The ultimatum game .................................. 10 1.6 Equilibria ......................................... 11 1.7 The centipede game ................................... 11 1.8 Subgames and subgame perfect equilibria ...................... 13 1.9 The dollar auction .................................... 14 1.10 Backward induction, Kuhn’s Theorem and a proof of Zermelo’s Theorem ... 15 2 Strategic form games 17 2.1 Definition ......................................... 17 2.2 Nash equilibria ...................................... 17 2.3 Classical examples .................................... 17 2.4 Dominated strategies .................................. 22 2.5 Repeated elimination of dominated strategies ................... 22 2.6 Dominant strategies ..................................
    [Show full text]
  • 1 Bertrand Model
    ECON 312: Oligopolisitic Competition 1 Industrial Organization Oligopolistic Competition Both the monopoly and the perfectly competitive market structure has in common is that neither has to concern itself with the strategic choices of its competition. In the former, this is trivially true since there isn't any competition. While the latter is so insignificant that the single firm has no effect. In an oligopoly where there is more than one firm, and yet because the number of firms are small, they each have to consider what the other does. Consider the product launch decision, and pricing decision of Apple in relation to the IPOD models. If the features of the models it has in the line up is similar to Creative Technology's, it would have to be concerned with the pricing decision, and the timing of its announcement in relation to that of the other firm. We will now begin the exposition of Oligopolistic Competition. 1 Bertrand Model Firms can compete on several variables, and levels, for example, they can compete based on their choices of prices, quantity, and quality. The most basic and funda- mental competition pertains to pricing choices. The Bertrand Model is examines the interdependence between rivals' decisions in terms of pricing decisions. The assumptions of the model are: 1. 2 firms in the market, i 2 f1; 2g. 2. Goods produced are homogenous, ) products are perfect substitutes. 3. Firms set prices simultaneously. 4. Each firm has the same constant marginal cost of c. What is the equilibrium, or best strategy of each firm? The answer is that both firms will set the same prices, p1 = p2 = p, and that it will be equal to the marginal ECON 312: Oligopolisitic Competition 2 cost, in other words, the perfectly competitive outcome.
    [Show full text]
  • Chapter 16 Oligopoly and Game Theory Oligopoly Oligopoly
    Chapter 16 “Game theory is the study of how people Oligopoly behave in strategic situations. By ‘strategic’ we mean a situation in which each person, when deciding what actions to take, must and consider how others might respond to that action.” Game Theory Oligopoly Oligopoly • “Oligopoly is a market structure in which only a few • “Figuring out the environment” when there are sellers offer similar or identical products.” rival firms in your market, means guessing (or • As we saw last time, oligopoly differs from the two ‘ideal’ inferring) what the rivals are doing and then cases, perfect competition and monopoly. choosing a “best response” • In the ‘ideal’ cases, the firm just has to figure out the environment (prices for the perfectly competitive firm, • This means that firms in oligopoly markets are demand curve for the monopolist) and select output to playing a ‘game’ against each other. maximize profits • To understand how they might act, we need to • An oligopolist, on the other hand, also has to figure out the understand how players play games. environment before computing the best output. • This is the role of Game Theory. Some Concepts We Will Use Strategies • Strategies • Strategies are the choices that a player is allowed • Payoffs to make. • Sequential Games •Examples: • Simultaneous Games – In game trees (sequential games), the players choose paths or branches from roots or nodes. • Best Responses – In matrix games players choose rows or columns • Equilibrium – In market games, players choose prices, or quantities, • Dominated strategies or R and D levels. • Dominant Strategies. – In Blackjack, players choose whether to stay or draw.
    [Show full text]
  • Dynamic Games Under Bounded Rationality
    Munich Personal RePEc Archive Dynamic Games under Bounded Rationality Zhao, Guo Southwest University for Nationalities 8 March 2015 Online at https://mpra.ub.uni-muenchen.de/62688/ MPRA Paper No. 62688, posted 09 Mar 2015 08:52 UTC Dynamic Games under Bounded Rationality By ZHAO GUO I propose a dynamic game model that is consistent with the paradigm of bounded rationality. Its main advantages over the traditional approach based on perfect rationality are that: (1) the strategy space is a chain-complete partially ordered set; (2) the response function is certain order-preserving map on strategy space; (3) the evolution of economic system can be described by the Dynamical System defined by the response function under iteration; (4) the existence of pure-strategy Nash equilibria can be guaranteed by fixed point theorems for ordered structures, rather than topological structures. This preference-response framework liberates economics from the utility concept, and constitutes a marriage of normal-form and extensive-form games. Among the common assumptions of classical existence theorems for competitive equilibrium, one is central. That is, individuals are assumed to have perfect rationality, so as to maximize their utilities (payoffs in game theoretic usage). With perfect rationality and perfect competition, the competitive equilibrium is completely determined, and the equilibrium depends only on their goals and their environments. With perfect rationality and perfect competition, the classical economic theory turns out to be deductive theory that requires almost no contact with empirical data once its assumptions are accepted as axioms (see Simon 1959). Zhao: Southwest University for Nationalities, Chengdu 610041, China (e-mail: [email protected]).
    [Show full text]
  • Extensive Form Games and Backward Induction
    Recap Perfect-Information Extensive-Form Games Extensive Form Games and Backward Induction ISCI 330 Lecture 11 February 13, 2007 Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 1 Recap Perfect-Information Extensive-Form Games Lecture Overview Recap Perfect-Information Extensive-Form Games Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 2 I The extensive form is an alternative representation that makes the temporal structure explicit. I Two variants: I perfect information extensive-form games I imperfect-information extensive-form games Recap Perfect-Information Extensive-Form Games Introduction I The normal form game representation does not incorporate any notion of sequence, or time, of the actions of the players Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 3 I Two variants: I perfect information extensive-form games I imperfect-information extensive-form games Recap Perfect-Information Extensive-Form Games Introduction I The normal form game representation does not incorporate any notion of sequence, or time, of the actions of the players I The extensive form is an alternative representation that makes the temporal structure explicit. Extensive Form Games and Backward Induction ISCI 330 Lecture 11, Slide 3 Recap Perfect-Information Extensive-Form Games Introduction I The normal form game representation does not incorporate any notion of sequence, or time, of the actions of the players I The extensive form is an alternative representation that makes the temporal
    [Show full text]
  • Restoring Fun to Game Theory
    Restoring Fun to Game Theory Avinash Dixit Abstract: The author suggests methods for teaching game theory at an introduc- tory level, using interactive games to be played in the classroom or in computer clusters, clips from movies to be screened and discussed, and excerpts from novels and historical books to be read and discussed. JEL codes: A22, C70 Game theory starts with an unfair advantage over most other scientific subjects—it is applicable to numerous interesting and thought-provoking aspects of decision- making in economics, business, politics, social interactions, and indeed to much of everyday life, making it automatically appealing to students. However, too many teachers and textbook authors lose this advantage by treating the subject in such an abstract and formal way that the students’ eyes glaze over. Even the interests of the abstract theorists will be better served if introductory courses are motivated using examples and classroom games that engage the students’ interest and encourage them to go on to more advanced courses. This will create larger audiences for the abstract game theorists; then they can teach students the mathematics and the rigor that are surely important aspects of the subject at the higher levels. Game theory has become a part of the basic framework of economics, along with, or even replacing in many contexts, the traditional supply-demand frame- work in partial and general equilibrium. Therefore economics students should be introduced to game theory right at the beginning of their studies. Teachers of eco- nomics usually introduce game theory by using economics applications; Cournot duopoly is the favorite vehicle.
    [Show full text]
  • MS&E 246: Lecture 10 Repeated Games
    MS&E 246: Lecture 10 Repeated games Ramesh Johari What is a repeated game? A repeated game is: A dynamic game constructed by playing the same game over and over. It is a dynamic game of imperfect information. This lecture • Finitely repeated games • Infinitely repeated games • Trigger strategies • The folk theorem Stage game At each stage, the same game is played: the stage game G. Assume: • G is a simultaneous move game •In G, player i has: •Action set Ai • Payoff Pi(ai, a-i) Finitely repeated games G(K) : G is repeated K times Information sets: All players observe outcome of each stage. What are: strategies? payoffs? equilibria? History and strategies Period t history ht: ht = (a(0), …, a(t-1)) where a(τ) = action profile played at stage τ Strategy si: Choice of stage t action si(ht) ∈ Ai for each history ht i.e. ai(t) = si(ht) Payoffs Assume payoff = sum of stage game payoffs Example: Prisoner’s dilemma Recall the Prisoner’s dilemma: Player 1 defect cooperate defect (1,1) (4,0) Player 2 cooperate (0,4) (2,2) Example: Prisoner’s dilemma Two volunteers Five rounds No communication allowed! Round 1 2 3 4 5 Total Player 1 1 1 1 1 1 5 Player 2 1 1 1 1 1 5 SPNE Suppose aNE is a stage game NE. Any such NE gives a SPNE: NE Player i plays ai at every stage, regardless of history. Question: Are there any other SPNE? SPNE How do we find SPNE of G(K)? Observe: Subgame starting after history ht is identical to G(K - t) SPNE: Unique stage game NE Suppose G has a unique NE aNE Then regardless of period K history hK , last stage has unique NE aNE NE ⇒ At SPNE, si(hK) = ai SPNE: Backward induction At stage K -1, given s-i(·), player i chooses si(hK -1) to maximize: Pi(si(hK -1), s-i(hK -1)) + Pi(s(hK)) payoff at stage K -1 payoff at stage K SPNE: Backward induction At stage K -1, given s-i(·), player i chooses si(hK -1) to maximize: NE Pi(si(hK -1), s-i(hK -1)) + Pi(a ) payoff at stage K -1 payoff at stage K We know: at last stage, aNE is played.
    [Show full text]
  • Alpha-Beta Pruning
    CMSC 474, Introduction to Game Theory Game-tree Search and Pruning Algorithms Mohammad T. Hajiaghayi University of Maryland Finite perfect-information zero-sum games Finite: finitely many agents, actions, states, histories Perfect information: Every agent knows • all of the players’ utility functions • all of the players’ actions and what they do • the history and current state No simultaneous actions – agents move one-at-a-time Constant sum (or zero-sum): Constant k such that regardless of how the game ends, • Σi=1,…,n ui = k For every such game, there’s an equivalent game in which k = 0 Examples Deterministic: chess, checkers go, gomoku reversi (othello) tic-tac-toe, qubic, connect-four mancala (awari, kalah) 9 men’s morris (merelles, morels, mill) Stochastic: backgammon, monopoly, yahtzee, parcheesi, roulette, craps For now, we’ll consider just the deterministic games Outline A brief history of work on this topic Restatement of the Minimax Theorem Game trees The minimax algorithm α-β pruning Resource limits, approximate evaluation Most of this isn’t in the game-theory book For further information, look at the following Russell & Norvig’s Artificial Intelligence: A Modern Approach • There are 3 editions of this book • In the 2nd edition, it’s Chapter 6 Brief History 1846 (Babbage) designed machine to play tic-tac-toe 1928 (von Neumann) minimax theorem 1944 (von Neumann & Morgenstern) backward induction 1950 (Shannon) minimax algorithm (finite-horizon search) 1951 (Turing) program (on paper) for playing chess 1952–7
    [Show full text]
  • Rationality Assumptions of Game Theory and the Backward Induction Paradox
    16 Rationality assumptions of game theory and the backward induction paradox Andrew M Col man Backward induction Backward induction is a form of logical reasoning, based on the technique of mathematical induction, that is applicable to certain sequential games. I shall illustrate it with a simple version of the ancient game of nim. There are 20 matches on the table, and two players take turns in removing either one or two matches, the winner being the player who takes the last one, leaving the other player unable to move. Ernst Zermelo (1912) proved the first major theorem of game theory to the effect that, in games of this type, either one player or the other must have a guaranteed winning strategy. In this case, which player wins, and how? The player who moves first wins. The game is easily solved by backward induction. We begin at the end: if it is my turn to move and there are either one or two matches left, then I can obviously win, because in either case I can immediately take the last match, leaving my opponent unable to move. Therefore, if it is my opponent's move and there are three matches left, I can win, because my opponent must take either one or two and will therefore have to leave either two or one, whereupon I can win immediately. Therefore, if it is my opponent's turn to move and there are six matches left, I can win, because my opponent will have to leave either four or five, and in either case I can then leave three, which as I have shown ensures that I can win.
    [Show full text]
  • Backward Induction, Or SPNE’S
    LECTURE 10: GAMES IN EXTENSIVE FORM Jan Zouhar Games and Decisions Sequential Move Games 2 so far, we have only dealt with simultaneous games (players make the decisions at the same time, or simply without knowing what the action of their opponent is) in most games played for amusement (cards, chess, other board games), players make moves in turns → sequential move games many economic problems are in the sequential form: English auctions price competition: firms repeatedly charge prices executive compensation (contract signed; then executive works) monetary authority and firms (continually observe and learn actions) … formally, we describe these as games in extensive form (representation using a game tree) Games and Decisions Jan Zouhar Class Game: Century Mark 3 rules: played by fixed pairs of players taking turns at each turn, each player chooses a number (integer) between 1 and 10 inclusive this choice is added to sum of all previous choices (initial sum is 0) the first player to take the cumulative sum above 100 (century) loses the game prize: 5 extra points for the final test (!!!) Volunteers? Games and Decisions Jan Zouhar Class Game: Century Mark (cont’d) 4 Analysis of the game what’s the winning strategy? broadly speaking, bring the sum to 89; then your opponent can’t possibly win actually, it’s enough to bring it to 78; then you can make sure to make it 89 later reasoning like this, the winning positions are: 100, 89, 78, 67, 56, 45, 34, 23, 12, 1 → the first mover can guarantee a win! winning strategy: in
    [Show full text]
  • Section Note 3
    Section Note 3 Ariella Kahn-Lang and Guthrie Gray-Lobe∗ February 13th 2013 Agenda 1. Game Trees 2. Writing out Strategies and the Strategy Space 3. Backwards Induction 1 Game Trees Let's review the basic elements of game trees (extensive form games). Remember, we can write any game in either its normal (matrix) form or its extensive (tree) form - which representation we use is mainly a question of which solution concept we want to implement. Game trees are particularly useful for representing dynamic (sequential) games, primarily be- cause they easily allow us to implement the simple solution concept of backwards induction (see later). 1.1 Dynamic Games vs. Simultaneous Games Many important economic applications in game theory cannot be described by a simultaneous move game. Recall that a simultaneous game is one where all players were choosing their actions without any information about actions chosen by other players. A dynamic game, in contrast, is one where at least one player at some point of the game is choosing his action with some information about actions chosen previously. While dynamic games are often sequential over time, what matters is not the timing, but the information a player holds about previous moves in the game, because this is what enables them to condition their strategy on previous moves. For this reason, the `order' in which we draw a game tree matters only in getting the flow of information correctly. In simultaneous games, we can draw the game tree either way round and it represents the same game. ∗Thanks to previous years' TF's for making their section materials available for adaptation.
    [Show full text]