# Discrete bidding games

@article{Develin2010DiscreteBG, title={Discrete bidding games}, author={Mike Develin and Sam Payne}, journal={Electron. J. Comb.}, year={2010}, volume={17} }

We study variations on combinatorial games in which, instead of alternating moves, the players bid with discrete bidding chips for the right to determine who moves next. We consider both symmetric and partisan games, and explore differences between discrete bidding games and Richman games , which allow real-valued bidding. Unlike Richman games, discrete bidding game variations of many familiar games, such as chess, Connect Four, and even Tic-Tac-Toe, are suitable for recreational play. We also… Expand

#### 19 Citations

Bidding games and efficient allocations

- Computer Science
- Games Econ. Behav.
- 2018

It is shown that PSPEs form a semilattice, with a unique and natural Bottom Equilibrium, showing the existence of pure subgame-perfect equilibria (PSPE). Expand

Discrete Richman-bidding scoring games

- Computer Science, Mathematics
- Int. J. Game Theory
- 2021

It is proved that for all sufficiently large heap sizes, the equilibrium outcomes of unitary games are eventually periodic, with period 2, and it is shown that the periodicity appears at the latest for heaps of sizes quadratic in the total budget. Expand

Determinacy in Discrete-Bidding Infinite-Duration Games

- Computer Science
- CONCUR
- 2019

This work studies the combination of discrete-bidding and infinite-duration games and proves that these games form a large determined subclass of concurrent games, where {\em determinacy} is the strong property that there always exists exactly one player who can guarantee winning the game. Expand

A Survey of Bidding Games on Graphs

- 2020

A graph game is a two-player zero-sum game in which the players move a token throughout a graph to produce an infinite path, which determines the winner or payoff of the game. In bidding games, both… Expand

Bidding Games and Efficient Allocations

- Computer Science, Economics
- EC
- 2015

It is shown that if the underlying game has the form of a binary tree, then there exists a natural PSPE with the following highly desirable properties: players' utility is weakly monotone in their budget, and a Pareto-efficient outcome is reached for any initial budget. Expand

Infinite-duration Bidding Games

- Computer Science
- J. ACM
- 2019

The key component of the proof is a quantitative solution to strongly connected mean-payoff bidding games in which the connection with random-turn games is extended to these games, and the higher bidder pays his bid to the other player and moves the token. Expand

Infinite-Duration Bidding Games

- Computer Science, Mathematics
- CONCUR
- 2017

The existence of threshold budgets are shown for a qualitative class of infinite-duration games, namely parity games, and a quantitative class, namely mean-payoff games, in which they extend the connection with random-turn games to theseGames, and construct explicit optimal strategies for both players. Expand

Infinite-Duration Poorman-Bidding Games

- Computer Science
- WINE
- 2018

The properties of poorman reachability games extend to complex qualitative objectives such as parity, similarly to the Richman case, and quantitative poorman games, namely poorman mean-payoff games, where they construct optimal strategies depending on the initial ratio, are presented. Expand

Endgames in bidding chess

- Mathematics
- 2017

Bidding chess is a chess variant where instead of alternating play, players bid for the opportunity to move. Generalizing a known result on so-called Richman games, we show that for a natural class… Expand

Bidding Mechanisms in Graph Games

- Mathematics, Computer Science
- MFCS
- 2019

The results show that Richman bidding is the exception; namely, for every $\tau <1$, the value of the game depends on the initial ratio. Expand

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