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 TITLE 19 EDUCATION PART 2 TEXAS EDUCATION AGENCY CHAPTER 111 TEXAS ESSENTIAL KNOWLEDGE AND SKILLS FOR MATHEMATICS SUBCHAPTER C HIGH SCHOOL RULE §111.46 Discrete Mathematics for Problem Solving, Adopted 2013 (One-Half to One Credit)
 (J) analyze the relative importance of the three desirable properties of fair division: equitability, envy-freeness, and Pareto optimality; and     (K) identify fair division procedures that exhibit envy-freeness.   (6) Game (or competition) theory. The student uses knowledge of basic game theory concepts to calculate optimal strategies. The student analyzes situations and identifies the use of gaming strategies. The student is expected to:     (A) recognize competitive game situations;     (B) represent a game with a matrix;     (C) identify basic game theory concepts and vocabulary;     (D) determine the optimal pure strategies and value of a game with a saddle point by means of the minimax technique;     (E) explain the concept of and need for a mixed strategy;     (F) compute the optimal mixed strategy and the expected value for a player in a game who has only two pure strategies;     (G) model simple two-by-two, bimatrix games of partial conflict;     (H) identify the nature and implications of the game called "Prisoners' Dilemma";     (I) explain the game known as "chicken";     (J) identify examples that illustrate the prevalence of Prisoners' Dilemma and chicken in our society; and     (K) determine when a pair of strategies for two players is in equilibrium.   (7) Theory of moves. The student analyzes the theory of moves (TOM). The student uses the TOM and game theory to analyze conflicts. The student is expected to:     (A) compare and contrast TOM and game theory;     (B) explain the rules of TOM;     (C) describe what is meant by a cyclic game;     (D) use a game tree to analyze a two-person game;     (E) determine the effect of approaching Prisoners' Dilemma and chicken from the standpoint of TOM and contrast that to the effect of approaching them from the standpoint of game theory;     (F) describe the use of TOM in a larger, more complicated game; and     (G) model a conflict from literature or from a real-life situation as a two-by-two strict ordinal game and compare the results predicted by game theory and by TOM. Source Note: The provisions of this §111.46 adopted to be effective August 25, 2014, 38 TexReg 9027

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