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Entrepreneurial Chess

Author

Listed:
  • Elwyn Berlekamp

    (Elwyn and Jennifer Berlekamp Foundation)

  • Richard M. Low

    (San Jose State University)

Abstract

Although the combinatorial game Entrepreneurial Chess (or Echess) was invented around 2005, this is our first publication devoted to it. A single Echess position begins with a Black king vs. a White king and a White rook on a quarter-infinite board, spanning the first quadrant of the xy-plane. In addition to the normal chess moves, Black is given the additional option of “cashing out”, which removes the board and converts the position into the integer $$x + y$$ x + y , where [x, y] are the coordinates of his king’s position when he decides to cash out. Sums of Echess positions, played on different boards, span an unusually wide range of topics in combinatorial game theory. We find many interesting examples.

Suggested Citation

  • Elwyn Berlekamp & Richard M. Low, 2018. "Entrepreneurial Chess," International Journal of Game Theory, Springer;Game Theory Society, vol. 47(2), pages 379-415, May.
    • Handle: RePEc:spr:jogath:v:47:y:2018:i:2:d:10.1007_s00182-017-0580-z
    DOI: 10.1007/s00182-017-0580-z
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    1. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(1), pages 193-194, February.
    2. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(2), pages 541-545, April.
    3. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(4), pages 1007-1017, August.
    4. ,, 2000. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 16(2), pages 287-299, April.
    5. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(6), pages 1461-1465, December.
    6. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(5), pages 1273-1289, October.
    7. ,, 2002. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 18(3), pages 819-821, June.
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    Keywords

    Combinatorial games; Chess;

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