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Full-Text Articles in Other Mathematics
Love Games: A Game-Theory Approach To Compatibility, Kerstin Bever, Julie Rowlett
Love Games: A Game-Theory Approach To Compatibility, Kerstin Bever, Julie Rowlett
Journal of Humanistic Mathematics
In this note, we present a compatibility test with a rigorous mathematical foundation in game theory. The test must be taken separately by both partners, making it difficult for either partner alone to control the outcome. To introduce basic notions of game theory we investigate a scene from the film "A Beautiful Mind" based on John Nash's life and Nobel-prize-winning theorem. We recall this result and reveal the mathematics behind our test. Readers may customize and modify the test for more accurate results or to evaluate interpersonal relationships in other settings, not only romantic. Finally, we apply Dyson's and Press's …
Extortion And Evolution In The Iterated Prisoner's Dilemma, Michael J. Earnest
Extortion And Evolution In The Iterated Prisoner's Dilemma, Michael J. Earnest
HMC Senior Theses
The Prisoner's Dilemma is a two player game where playing rationally leads to a suboptimal outcome for both players. The game is simple to analyze, but when it is played repeatedly, complex dynamics emerge. Recent research has shown the existence of extortionate strategies, which allow one player to win at least as much as the other. When one player plays such a strategy, the other must either decide to take a low payoff, or accede to the extortion, where they earn higher payoff, but their opponent receives a larger share. We investigate what happens when one player uses this strategy …
Book Review: Across The Board: The Mathematics Of Chessboard Problems By John J. Watkins, Arthur T. Benjamin
Book Review: Across The Board: The Mathematics Of Chessboard Problems By John J. Watkins, Arthur T. Benjamin
All HMC Faculty Publications and Research
I think I became a mathematician because I loved to play games as a child. I learned about probability and expectation by playing games like backgammon, bridge, and Risk. But I experienced the greater thrill of careful deductive reasoning through games like Mastermind and chess. In fact, for many years I took the game of chess quite seriously and played in many tournaments. But I gave up the game when I started college and turned my attention to more serious pursuits, like learning real mathematics.
Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman
Analysis Of The N-Card Version Of The Game Le Her, Arthur T. Benjamin, Alan J. Goldman
All HMC Faculty Publications and Research
We present a complete solution to a card game with historical origins. Our analysis exploits the convexity properties in the payoff matrix, allowing this discrete game to be resolved by continuous methods.
The Best Way To Knock 'M Down, Arthur T. Benjamin, Matthew T. Fluet '99
The Best Way To Knock 'M Down, Arthur T. Benjamin, Matthew T. Fluet '99
All HMC Faculty Publications and Research
"Knock 'm Down" is a game of dice that is so easy to learn that it is being played in classrooms around the world. Although this game has been effective at developing students' intuition about probability [Fendel et al. 1997; Hunt 1998], we will show that lurking underneath this deceptively simple game are many surprising and highly unintuitive results.
Bounds On A Bug, Arthur T. Benjamin, Matthew T. Fluet '99
Bounds On A Bug, Arthur T. Benjamin, Matthew T. Fluet '99
All HMC Faculty Publications and Research
In the game of Cootie, players race to construct a "cootie bug" by rolling a die to collect component parts. Each cootie bug is composed of a body, a head, two eyes, one nose, two antennae, and six legs. Players must first acquire the body of the bug by rolling a 1. Next, they must roll a 2 to add the head to the body. Once the body and head are both in place, the remaining body parts can be obtained in any order by rolling two 3s for the eyes, one 4 for the nose, two 5s for the …
Optimal Klappenspiel, Arthur T. Benjamin, Derek Stanford '93
Optimal Klappenspiel, Arthur T. Benjamin, Derek Stanford '93
All HMC Faculty Publications and Research
The game Klappenspiel ("flipping game") is a traditional German game of flipping tiles according to dice rolls. In this paper, we derive the optimal strategy for this game by using dynamic programming. We show that the probability of winning using the optimal strategy is 0.30%.