Level-k reasoning and time pressure in the 11–20 money request game

Lindnera, Florian, and Matthias Sutter. “Level-k reasoning and time pressure in the 11–20 money request game." Economics Letters (2013). PDF (359 K) form Economics Letters ; working paper version: uibk.ac.at 提供的 [PDF];

==Notes by yinung==

什麼是 11–20 money request game

兩人一組player 1 and player 2, 每人選一個數字 x1, x2  ~ [11,20]。每人將得到 x_i, i=1, 2; 但如果 x_i < x_j 且 x_i +1 = x_j (即所選的數字比對手恰好少 1), 則 player i 將額外獲得 20 的 bonus.

原文:
The 11–20 money request game of AR (Arad and Rubinstein (2012a)) is a simultaneous move game in which two players request a number of points between 11 and 20, which they receive for sure. One player may receive 20 extra points if he/she requests one point less than the other player does.

主要結論

一般人通常是 level-0 到 level-k 的思考.

重覆 game 並不會有 learning 的現象

時間有壓力 (只有 15 sec.  v.s. 3 min.), 結果更接近理論值 (思考快, 直覺上會有更深的 level thinking)

Selected experimental results

Treatment 的設計

BASE: 重覆 AR (2012, AER)
BASE-T: 和 TIME 一樣, 但是時間給 3 min ( v.s. 15 秒)
TIME: (有時間壓力) 遊戲開始才知道要選 [11,20]、bonus =20 和其條件。 決策時間只有 15 秒

R-BASE、R-BASE-T、R-TIME 是以上的 one-shot game, 重覆玩5回合 (每回合3 min, 除了 R-TIME 是 15秒)

Table 1. Relative frequencies of actions in different treatments.
Action 11 (%) 12 (%) 13 (%) 14 (%) 15 (%) 16 (%) 17 (%) 18 (%) 19 (%) 20 (%) N
Equilibrium 25 25 20 15 10 5
AR (2012) 4 0 3 6 1 6 32 30 12 6 108
BASE 1 3 4 6 3 6 20 38 14 6 80
BASE-T 4 1 1 8 6 5 15 34 19 8 80
TIME 3 3 11 5 20 5 18 17 11 8 65
Table 2. Actions in the repeated game.
Action 11 (%) 12 (%) 13 (%) 14 (%) 15 (%) 16 (%) 17 (%) 18 (%) 19 (%) 20 (%) N
Equilibrium 25 25 20 15 10 5
R-BASE 0 1 2 2 7 11 20 24 21 13 400
R-BASE-T 1 3 2 4 8 9 21 22 18 12 400
R-TIME 3 3 3 5 8 11 18 24 12 13 325

Abstract

Arad and Rubinstein (2012a) have designed a novel game to study level-k

reasoning experimentally. Just like them, we find that the depth of reasoning is very limited and clearly different from that in equilibrium play. We show that such behavior is even robust to repetitions; hence there is, at best, little learning. However, under time pressure, behavior is, perhaps coincidentally, closer to that in equilibrium play. We argue that time pressure evokes intuitive reasoning and reduces the focal attraction of choosing higher (and per se more profitable) numbers in the game.

JEL classification

  • C91;
  • C72

References (from EL)

    • Greiner, 2004, Ben. Greiner, An online recruitment system for economic experiments, Kurt Kremer, Volker Macho (Eds.), Forschung und Wissenschaftliches Rechnen 2003, Gesellschaft für Wissenschaftliche Datenverarbeitung Göttingen, Göttingen (2004), pp. 79–93.View Record in Scopus| Cited By in Scopus (1)
    • Nagel, 1995, Rosemarie Nagel, Unraveling in guessing games: an experimental study, American Economic Review, 85 (5) (1995), pp. 1313–1326.
    • Roth and Ockenfels, 2002, Alvin E. Roth, Axel Ockenfels, Last-minute bidding and the rules for ending second-price auctions: evidence from eBay and Amazon auctions on the internet, American Economic Review, 92 (5) (2002), pp. 1138–1151.
    • Stahl and Wilson, 1995, Dale O. Stahl, Paul W. Wilson, On players’ models of other players: theory and experimental evidence, Games and Economic Behavior, 10 (1) (1995), pp. 213–254.
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