# Game with predatory player (reference request)

I am interested in a multiplayer game where one player gains utility, not just by winning, but by seeing one other player (chosen in advance) lose (or come in last place if the game has an ordered finish). Obviously, the best case scenario for this player would be to win and his 'prey' to come in last, and the worst case scenario is where he comes in last and his 'prey' wins. I wanted to look at two scenarios. The first scenario is where the 'prey' does not know that they are being targeted, and the second scenario is where they do know. I have looked for a paper with a similar style game, but have been unsuccessful. Does anyone know if a game like this has been analyzed? Your help would be greatly appreciated.

Note that this is different from a Zero-Sum game in a Predation Model

Also, if there has been no work done on this, do you think this would be an interesting game to analyze, and would it have any real world applications?

• This information can be perfectly incorporated into the payoff function. Say the payoff function of player $i$ is $f_i(r_i,r_p) = r_p - r_i$, where $r_i$ is his ranking and $r_p$ is the ranking of her prey, player $p$. Other similar payoff functions can also be constructed to better reflect the relationship between $r_i$ and $r_p$ you have in mind. Nov 24, 2015 at 16:28
• If you have a specific competition model with actions by the players in mind note that you will also have to explain how the prey "does not know that they are being targeted". Is there a type space, or is this a case of bounded rationality, unawareness, etc. Nov 24, 2015 at 16:29
• That is so obvious, and I'm kind of embarrassed for not thinking to incorporate the predation into the agent's payoff function. Thank you so much! Now, I just need to look for games with a predatory payoff function (which should narrow down my search because predation games kept coming up in my previous searches). Nov 24, 2015 at 16:34
• Probably not 100% what you're looking for, but there is some small literature (most not from economists) on "malicious players" in congestion games who act with malice towards the other players. Nov 24, 2015 at 17:42
• This sounds remeniscent of auctions with externalities (i.e. auctions which units they win, but also about who wins any units they don't). For example a bidder in a (e.g. spectrum) license auction might care about which firms win the other operating licenses because it will have to compete with those firms in the future. Nov 25, 2015 at 9:51