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Created July 6, 2015 12:04
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Discussion of issues in applying risk aversion and logit choice in common-values auctions.
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"<h3>Bidding in interdependent-values auctions</h3>\n",
"<h4>Notes on fitting logit quantal response models in private and common values auctions</h4>\n",
"\n",
"Theodore L. Turocy\n",
"\n",
"This version 2015-07-06."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"These are notes in support of the logit quantal response estimations being carried out as part of Turocy and Cason, \"Bidding in first-price and second-price interdependent-values auctions:\n",
"A laboratory experiment\"\n",
"\n",
"We are interested in how bidding behaviour changes as valuations in auctions become more interdependent, and using this to compare models developed in the private-values domain (risk aversion and regret) versus those for the common-values domain (cursedness).\n",
"\n",
"The main theme here is the struggle to make a model with risk aversion coherent within the logit choice framework. There are two issues:\n",
"\n",
"* The workhorse CRRA model from first-price private-values auctions blows up when losses are possible. The most straightforward thing to do is to take a cue from prospect theory, and simply reflect the utility function through the origin: that is, if the payoff to gains is proportional to $x^{1-r}$, then the payoff to losses is proportional to $-|x|^{1-r}$. We show that this risk aversion in losses has a perhaps undesirable effect when thinking about defining logit choice probabilities.\n",
"* Compounding this, in the case of the common-value auction we study (in which the common value is the average of the two signals), the payoff functions for risk-neutral and risk-averse bidders do not differ markedly in the gains domain. However, they differ substantially in the loss domain, owing primarily to the choice of reflection as above. Therefore, any model attempting to estimate risk attitude due to this specification, will be driven entirely by the presence of very aggressive bids in the bidder's dataset, which seems unattractive.\n",
"\n",
"The calculations below attempt to outline these issues in a succinct way."
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"import pandas\n",
"import numpy as np\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"alldata = pandas.read_csv(\"../data/alldata.csv\")\n",
"# Rescale bids and signals to be in pence (so they are integers)\n",
"for col in [ 'own_signal', 'own_bid', 'other_signal', 'other_bid' ]:\n",
" alldata[col] = alldata[col].apply(lambda x: int(round(x*100))).astype(int)\n",
"\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Private values\n",
"First, we explore the implications of risk aversion and regret in the familiar FPA-PV setting."
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"df = alldata[(alldata.is_fpa==1) & (alldata.treatment==\"PV\")].copy()"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"# Construct empirical distribution of other (signal, bid) pairs\n",
"df['key'] = 1\n",
"grid = pandas.DataFrame([ [ signal, bid, 1 ]\n",
" for signal in np.arange(20, 1001, 20)\n",
" for bid in np.arange(10, 1001, 10) ],\n",
" columns=[ 'signal', 'bid', 'key' ])\n",
"hypo = pandas.merge(grid,\n",
" df[[\"gamma\", \"other_signal\", \"other_bid\", \"key\"]],\n",
" how='outer', left_on='key', right_on='key')\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"At this point, `hypo` contains all possible (signal, bid) pairs for a bidder, matched up with all realizations of bids and signals from the actual data.\n",
"\n",
"Previous estimates tend to suggest risk-aversion parameters around $r=0.5$, so let's use that."
]
},
{
"cell_type": "code",
"execution_count": 26,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"rho = 0.5\n",
"alp = 0.5\n",
"chi = 0.0\n",
"hypo[\"value_true\"] = (1.0-hypo.gamma)*hypo.signal + hypo.gamma*hypo.other_signal\n",
"hypo[\"value_cursed\"] = (1.0-hypo.gamma)*hypo.signal + hypo.gamma*500\n",
"hypo[\"purchase\"] = (hypo.bid > hypo.other_bid).astype(int) + \\\n",
" 0.5*((hypo.bid == hypo.other_bid).astype(int))\n",
"hypo[\"payoff_rn\"] = hypo[\"purchase\"] * (hypo[\"value_true\"] - hypo[\"bid\"])\n",
"hypo[\"payoff_ra\"] = hypo[\"purchase\"] / (1.0-rho) * (hypo[\"value_true\"] - hypo[\"bid\"])**(1.0-rho)\n",
"losses = hypo[hypo[\"value_true\"] < hypo[\"bid\"]]\n",
"hypo.loc[hypo[\"value_true\"] - hypo[\"bid\"]<0,\"payoff_ra\"] = -losses[\"purchase\"] / (1.0-rho) * (losses[\"bid\"] - losses[\"value_true\"])**(1.0-rho)\n",
"hypo[\"payoff_ra\"] = hypo[\"payoff_ra\"] / (1.0-rho) * 10.0**(1.0-rho)\n",
"\n",
"hypo[\"loser_regret\"] = (hypo.value_true-hypo.other_bid).clip(lower=0)\n",
"\n",
"hypo[\"payoff_reg\"] = -hypo.loser_regret*(1.0-hypo.purchase)\n",
"hypo[\"payoff_rnreg\"] = (1.0-alp) * hypo.payoff_rn + alp * hypo.payoff_reg\n",
"payoffs = hypo.groupby([ 'signal', 'bid' ]).mean().reset_index()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For starters, let's look at a bidder with signal 500, which is exactly the midpoint of the distribution of signals.\n",
"\n",
"In the gains domain, we see the familiar shifting of the best-response to higher bids. However, the inflection point is very clear above bids of 500. The risk-loving behaviour in losses implies a loss of 500 (from, say, bidding 1000 and winning) is not that much worse than a loss of 490 (from bidding 990 and winning). This of course has no impact on the best response; however, it does have an impact on the logit choice distribution. Very large bids are going to be more consistent with large values of $\\rho$. This is not a big problem for the FPA-PV, where there are very few bids above signal, but is perhaps more problematic in the common-value case, as we will discuss below.\n",
"\n",
"For comparison we also plot the objective of a regret-minimising bidder, which obviously is monotonically increasing and reaches its maximum at the signal, 500. The regret-bidder specification we use is a linear combination of the regret-minimiser and risk-neutral; we plot the curve for a bidder with regret parameter 0.5.\n",
"\n",
"Roughly speaking, the regret model is more tolerant overall of bids above value (the utility curve falls off less steeply for the regret model than the risk-averse one), but it penalises each bid increment above the private value equally."
]
},
{
"cell_type": "code",
"execution_count": 28,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x11177b090>"
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"execution_count": 28,
"metadata": {},
"output_type": "execute_result"
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{
"data": {
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9X1/sK2v/XBVSZRL1HEhL47GwMK7m53OmeXMGVq9e+YPCtm3QtKlYwuLHH2VQ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\nxb7/AwRDPVlud704AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112701990>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(payoffs[payoffs.signal==500]['bid'], payoffs[payoffs.signal==500]['payoff_rn'], label='Risk neutral')\n",
"plt.plot(payoffs[payoffs.signal==500]['bid'], payoffs[payoffs.signal==500]['payoff_ra'], label='Risk averse')\n",
"plt.plot(payoffs[payoffs.signal==500]['bid'], payoffs[payoffs.signal==500]['payoff_reg'], label='Regret 1.0')\n",
"plt.plot(payoffs[payoffs.signal==500]['bid'], payoffs[payoffs.signal==500]['payoff_rnreg'], label='Regret 0.5')\n",
"plt.legend(loc='lower left')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can also run the comparison for a medium-high signal, such as 800."
]
},
{
"cell_type": "code",
"execution_count": 30,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1121d0950>"
]
},
"execution_count": 30,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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l8WVcHEdycnjU359x/v7U+09/0qJFur/hm2/0muvnKaUI+jiIjaM20sy7WQWX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\nIiIiIiIiIiIiIiIikvv+D+D2Xn0+du6+AAAAAElFTkSuQmCC\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112044410>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(payoffs[payoffs.signal==800]['bid'], payoffs[payoffs.signal==800]['payoff_rn'], label='RN')\n",
"plt.plot(payoffs[payoffs.signal==800]['bid'], payoffs[payoffs.signal==800]['payoff_ra'], label='RA')\n",
"plt.plot(payoffs[payoffs.signal==800]['bid'], payoffs[payoffs.signal==800]['payoff_reg'], label='Regret 1.0')\n",
"plt.plot(payoffs[payoffs.signal==800]['bid'], payoffs[payoffs.signal==800]['payoff_rnreg'], label='Regret 0.5')\n",
"plt.legend(loc='lower right')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Common values\n",
"Now let's consider the pure common-values case. The next several cells replicate the calculations as above."
]
},
{
"cell_type": "code",
"execution_count": 35,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"df = alldata[(alldata.is_fpa==1) & (alldata.treatment==\"CV\")].copy()"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"# Construct empirical distribution of other (signal, bid) pairs\n",
"df['key'] = 1\n",
"grid = pandas.DataFrame([ [ signal, bid, 1 ]\n",
" for signal in np.arange(20, 1001, 20)\n",
" for bid in np.arange(10, 1001, 10) ],\n",
" columns=[ 'signal', 'bid', 'key' ])\n",
"hypo = pandas.merge(grid,\n",
" df[[\"gamma\", \"other_signal\", \"other_bid\", \"key\"]],\n",
" how='outer', left_on='key', right_on='key')"
]
},
{
"cell_type": "code",
"execution_count": 39,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"rho = 0.5\n",
"alp = 0.5\n",
"chi = 0.0\n",
"hypo[\"value_true\"] = (1.0-hypo.gamma)*hypo.signal + hypo.gamma*hypo.other_signal\n",
"hypo[\"value_cursed\"] = (1.0-hypo.gamma)*hypo.signal + hypo.gamma*500\n",
"hypo[\"purchase\"] = (hypo.bid > hypo.other_bid).astype(int) + \\\n",
" 0.5*((hypo.bid == hypo.other_bid).astype(int))\n",
"hypo[\"payoff_rn\"] = hypo[\"purchase\"] * (hypo[\"value_true\"] - hypo[\"bid\"])\n",
"hypo[\"payoff_ra\"] = hypo[\"purchase\"] / (1.0-rho) * (hypo[\"value_true\"] - hypo[\"bid\"])**(1.0-rho)\n",
"losses = hypo[hypo[\"value_true\"] < hypo[\"bid\"]]\n",
"hypo.loc[hypo[\"value_true\"] - hypo[\"bid\"]<0,\"payoff_ra\"] = -losses[\"purchase\"] / (1.0-rho) * (losses[\"bid\"] - losses[\"value_true\"])**(1.0-rho)\n",
"hypo[\"payoff_ra\"] = hypo[\"payoff_ra\"] / (1.0-rho) * 10.0**(1.0-rho)\n",
"\n",
"hypo[\"loser_regret\"] = (hypo.value_true-hypo.other_bid).clip(lower=0)\n",
"\n",
"hypo[\"payoff_reg\"] = -hypo.loser_regret*(1.0-hypo.purchase)\n",
"hypo[\"payoff_rnreg\"] = (1.0-alp) * hypo.payoff_rn + alp * hypo.payoff_reg\n",
"hypo[\"payoff_cursed\"] = hypo[\"purchase\"] * (hypo[\"value_cursed\"] - hypo[\"bid\"])\n",
"payoffs = hypo.groupby([ 'signal', 'bid' ]).mean().reset_index()"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now for the main event: the decision utility curves for signal 500.\n",
"\n",
"Observe that the curves for the risk-neutral and risk-averse bidders coincide almost perfectly in the gains domain. This is indeed consistent with the theoretical result of Holt and Sherman, who show that in this game the equilibrium is independent of risk attitudes. In the loss domain, however, they diverge as before.\n",
"\n",
"The implication of this is important enough I'll put it in boldface type: **In fitting a logit response, the only data which will distinguish the risk-neutral and constant-relative risk attitude model with reflection around the origin, are bids which are so aggressive they (almost) always lose money.** This implies that the interpretation of an estimated coefficient $\\hat\\rho$ in FPA-CV is rather different than it is in FPA-PV.\n",
"\n",
"We also here now show the decision utility for the fully cursed bidder. This illustrates that cursedness versus non-cursedness is going to be driven by whether bids tend to be in the 300s versus the 200s for this bidder."
]
},
{
"cell_type": "code",
"execution_count": 40,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x1129fe6d0>"
]
},
"execution_count": 40,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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u5IEDoVcvEN9GKy0rC2Z0y+XptEh6/tUWVQcVOoOO+Qfm8234t2was4lePr2q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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x112e0e350>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(payoffs[payoffs.signal==500]['bid'], payoffs[payoffs.signal==500]['payoff_rn'], label='Risk neutral')\n",
"plt.plot(payoffs[payoffs.signal==500]['bid'], payoffs[payoffs.signal==500]['payoff_ra'], label='Risk averse')\n",
"plt.plot(payoffs[payoffs.signal==500]['bid'], payoffs[payoffs.signal==500]['payoff_reg'], label='Regret 1.0')\n",
"plt.plot(payoffs[payoffs.signal==500]['bid'], payoffs[payoffs.signal==500]['payoff_rnreg'], label='Regret 0.5')\n",
"plt.plot(payoffs[payoffs.signal==500]['bid'], payoffs[payoffs.signal==500]['payoff_cursed'], label='Cursed')\n",
"\n",
"plt.legend(loc='lower left')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"For comparability, let's also look at signal 800. Here we see that the risk neutral and risk averse payoffs do not coincide precisely when bidding is not in equilibrium, but nevertheless there will be very little to distinguish them in the gains domain; it will be only the very aggressive bids above signal which contribute to any likelihood difference in the estimation."
]
},
{
"cell_type": "code",
"execution_count": 42,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x113c6dc90>"
]
},
"execution_count": 42,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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H8WgqNXh+4E2UnT07/1Rw8SJERcmJwNZW7k5qYgJ2dvDww9CzlwbXtnGczzvK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\nCCGEEEIIy/e/ybY2cO9sqJ8AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x113c6de90>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(payoffs[payoffs.signal==800]['bid'], payoffs[payoffs.signal==800]['payoff_rn'], label='Risk neutral')\n",
"plt.plot(payoffs[payoffs.signal==800]['bid'], payoffs[payoffs.signal==800]['payoff_ra'], label='Risk averse')\n",
"plt.plot(payoffs[payoffs.signal==800]['bid'], payoffs[payoffs.signal==800]['payoff_reg'], label='Regret 1.0')\n",
"plt.plot(payoffs[payoffs.signal==800]['bid'], payoffs[payoffs.signal==800]['payoff_rnreg'], label='Regret 0.5')\n",
"plt.plot(payoffs[payoffs.signal==800]['bid'], payoffs[payoffs.signal==800]['payoff_cursed'], label='Cursed')\n",
"plt.legend(loc='lower left')"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 2",
"language": "python",
"name": "python2"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 2
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython2",
"version": "2.7.9"
}
},
"nbformat": 4,
"nbformat_minor": 0
}
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